美国《 数学评论》数据库（MRDB, http://www.ams.org/home/page ）题录数论研究文献，先后已经有几篇博文进行过报道：如 2012 年 4 月份 MRDB 题录数论最新文献 246 篇 ， http://www.ams.org/home/page ； 5 月份 MRDB 题录数论最新研究文献 311 篇， http://www.ams.org/home/page ； 6 月份 MRDB 题录数学文献 15957 篇，其中题录数论最新文献 234 篇，更多信息请浏览附件 June 2012-Number theory.pdf ； 7 月份 MRDB 题录数学文献 9066 篇，其中 题录数论最新文献273 篇 ； 8 月份 MRDB 题录数学文献 10720 篇，其中 题录数论最新文献 333 篇， http://blog.sciencenet.cn/blog-212210-608354.html ； 9 月份 MRDB 题录数学文献9 161 篇，其中 题录数论最新文献174篇 ； 下面列出部分题录结果，更多信息请浏览附件。 MR2962318 Nekovář, Jan Level raising and anticyclotomic Selmer groups for Hilbert modular forms of weight two. Canad. J. Math. 64 (2012), no. 3, 588–668. MR2962312 Havil, Julian The irrationals. Princeton University Press, Princeton, NJ, 2012. xii+298 pp. ISBN: 978-0-691-14342-2 MR2962243 Hassani, Mehdi Factorization of factorials and a result of Hardy and Ramanujan. Math. Inequal. Appl. 15 (2012), no. 2, 403–407. MR2922349 Jones, Lenny Corrigendum to "Polynomial Cunningham chains'' . J. 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W. ; Zeng, Jiang Proof of some conjectures of Z.-W. Sun on congruences for Apéry polynomials. J. Number Theory 132 (2012), no. 8, 1731–1740. MR2922340 Thiel, Carsten Adelic geometry and polarity. J. Number Theory 132 (2012), no. 8, 1720–1730. MR2922339 Bradshaw, Robert ; Stein, William Heegner points and the arithmetic of elliptic curves over ring class extensions. J. Number Theory 132 (2012), no. 8, 1707–1719. MR2922338 Pintér, kos ; Ziegler, Volker ON arithmetic progressions in recurrences—a new characterization of the Fibonacci sequence. J. Number Theory 132 (2012), no. 8, 1686–1706. MR2922336 Diaz y Diaz, Francisco ; Friedman, Eduardo Colmez cones for fundamental units of totally real cubic fields. J. Number Theory 132 (2012), no. 8, 1653–1663. MR2922335 Bayad, Abdelmejid ; Raouj, Abdelaziz Mean values of L -functions and Dedekind sums. J. Number Theory 132 (2012), no. 8, 1645–1652. MR2921617 Degroote, Claudia ; Demeyer, Jeroen Hilbert's tenth problem for rational function fields over p -adic fields. J. Algebra 361 (2012), 172–187. MR2921609 O'Shea, James Isotropy over function fields of Pfister forms. J. Algebra 361 (2012), 23–36. MR2920834 Tauraso, Roberto q -analogs of some congruences involving Catalan numbers. Adv. in Appl. Math. 48 (2012), no. 5, 603–614. MR2910353 Adell, José A. Estimates of generalized Stieltjes constants with a quasi-geometric rate of decay. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 468 (2012), no. 2141, 1356–1370. MR2921257 Badshah, V. H. ; Teeth, Manjeet Singh ; Dar, Mohsen Maqbool Generalized Fibonacci-like sequence and its properties. Int. J. Contemp. Math. Sci. 7 (2012), no. 21-24, 1155–1164. MR2921165 Gurevich, Shamgar ; Hadani, Ronny The Weil representation in characteristic two. Adv. Math. 230 (2012), no. 3, 894–926. MR2921161 Paule, Peter ; Radu, Cristian-Silviu The Andrews-Sellers family of partition congruences. Adv. 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MR2920885 Fouquet, Olivier ; Ochiai, Tadashi Control theorems for Selmer groups of nearly ordinary deformations. J. Reine Angew. Math. 666 (2012), 163–187. MR2920881 Pilloni, Vincent Modularité, formes de Siegel et surfaces abéliennes. (French) J. Reine Angew. Math. 666 (2012), 35–82. MR2917241 Srivastava, Bhaskar Some identities connected with a continued fraction of Ramanujan. Taiwanese J. Math. 16 (2012), no. 3, 829–838. MR2917077 Murty, M. Ram ; Murty, V. Kumar Transcendental values of class group L -functions, II. Proc. Amer. Math. Soc. 140 (2012), no. 9, 3041–3047. MR2917076 Cyr, Van A number theoretic question arising in the geometry of plane curves and in billiard dynamics. Proc. Amer. Math. Soc. 140 (2012), no. 9, 3035–3040. MR2917075 Kedlaya, Kiran S. A construction of polynomials with squarefree discriminants. Proc. Amer. Math. Soc. 140 (2012), no. 9, 3025–3033. MR2917071 Brumer, Armand ; Kramer, Kenneth Arithmetic of division fields. Proc. Amer. Math. Soc. 140 (2012), no. 9, 2981–2995. MR2917068 Huang, I-Chiau Algebraic structures of Euler numbers. Proc. Amer. Math. Soc. 140 (2012), no. 9, 2945–2952. MR2961790 Liu, Ruochuan ; Xie, Bingyong ; Zhang, Yuancao Locally analytic vectors of unitary principal series of G L 2 ( Q p ) . Ann. Sci. c. Norm. Supér. (4) 45 (2012), no. 1, 167–170. MR2961617 Choi, J. ; Kim, D. S. ; Kim, T. ; Kim, Y. H. Some arithmetic identities on Bernoulli and Euler numbers arising from the p -adic integrals on Z p . Adv. Stud. Contemp. Math. (Kyungshang) 22 (2012), no. 2, 239–247. MR2961615 Kim, Dae San Simple recursive formulas generating power moments of Kloosterman sums. Adv. Stud. Contemp. Math. (Kyungshang) 22 (2012), no. 2, 225–231. 更多信息请浏览附件 MR2012-09-174 for Number Theory.pdf
对于美国《数学评论》题录数论研究文献，从 2012 年 4 月延安会议之后，就已经开始关注，先后由几篇博文进行过报道：如 2012 年 4 月份 MR 题录数论最新文献 246 篇 ， http://blog.sciencenet.cn/blog-212210-568217.html ； 5 月份 MR 题录数论最新研究文献 311 篇， http://blog.sciencenet.cn/blog-212210-577496.html ； 6 月份 MR 题录数学文献 15957 篇，其中题录数论最新文献 234 篇，更多信息请浏览附件 June 2012-Number theory.pdf ； 7 月份 MR 题录数学文献 9066 篇，其中 题录数论最新文献273 篇 ； 8 月份 MR 题录数学文献 10720 篇，其中 题录数论最新文献 333 篇 ；下面列出部分题录结果，更多信息请浏览附件。 MR2951975 Wang, Tingting ; Zhang, Wenpeng Some identities involving Fibonacci, Lucas polynomials and their applications. Bull. Math. Soc. Sci. Math. Roumanie (N.S.) 55(103) (2012), no. 1, 95–103. MR2951974 Tall, Amadou A generalization of the Lucas addition chains. Bull. Math. Soc. Sci. Math. Roumanie (N.S.) 55(103) (2012), no. 1, 79–93. MR2951973 Stan, Florin ; Zaharescu, Alexandru The Siegel norm of algebraic numbers. Bull. Math. Soc. Sci. Math. Roumanie (N.S.) 55(103) (2012), no. 1, 69–77. MR2951971 Kilic, Emrah ; Akkus, Ilker ; Ohtsuka, Hideyuki Some generalized Fibonomial sums related with the Gaussian q -binomial sums. Bull. Math. Soc. Sci. Math. Roumanie (N.S.) 55(103) (2012), no. 1, 51–61. MR2951734 Reynolds, Jonathan Perfect powers generated by the twisted Fermat cubic. Funct. Approx. Comment. Math. 46 (2012), part 1, 133–145. ISBN: 978-83-232-2386-3 MR2951732 Gica, Alexandru ; Luca, Florian On the Diophantine equation 2 x = x 2 + y 2 −2 . Funct. Approx. Comment. Math. 46 (2012), part 1, 109–116. ISBN: 978-83-232-2386-3 MR2951731 Boklan , Kent D. ; Wooley, Trevor D. On Weyl sums for smaller exponents. Funct. Approx. Comment. Math. 46 (2012), part 1, 91–107. ISBN: 978-83-232-2386-3 MR2951730 Kozuka, Kazuhito A combinatorial-geometric viewpoint of Knopp's formula for Dedekind sums. Funct. Approx. Comment. Math. 46 (2012), part 1, 79–89. ISBN: 978-83-232-2386-3 MR2951728 Bayad, Abdelmejid ; Hamahata, Yoshinori Multiple polylogarithms and multi-poly-Bernoulli polynomials. Funct. Approx. Comment. Math. 46 (2012), part 1, 45–61. ISBN: 978-83-232-2386-3 MR2951727 Mahadeva Naika, M. S. ; Chandankumar, S. ; Bairy, K. Sushan New identities for Ramanujan's cubic continued fraction. Funct. Approx. Comment. Math. 46 (2012), part 1, 29–44. ISBN: 978-83-232-2386-3 MR2951726 Tzermias, Pavlos On Cauchy-Liouville-Mirimanoff polynomials II. Funct. Approx. Comment. Math. 46 (2012), part 1, 15–27. ISBN: 978-83-232-2386-3 MR2951725 Zhang, Zhongfeng Powers in ∏ n k =1 ( ak 2 l ⋅ 3 m + b ) . Funct. Approx. Comment. Math. 46 (2012), part 1, 7–13. ISBN: 978-83-232-2386-3 MR2908784 Matthiesen, Lilian Correlations of the divisor function. Proc. Lond. Math. Soc. (3) 104 (2012), no. 4, 827–858. MR2908782 Lagarias, J. C. ; Soundararajan, K. Counting smooth solutions to the equation A + B = C . Proc. Lond. Math. Soc. (3) 104 (2012), no. 4, 770–798. MR2908781 Kurihara, Masato Refined Iwasawa theory and Kolyvagin systems of Gauss sum type. Proc. Lond. Math. Soc. (3) 104 (2012), no. 4, 728–769. MR2903831 Lee, H. Y. ; Jung, N. S. ; Ryoo, C. S. Generalized w -Euler numbers and polynomials. ISRN Appl. Math. 2012, Art. ID 475463, 14 pp. MR2903585 Sazegar, Hashem A method for solving Legendre's conjecture. J. Math. Res. 4 (2012), no. 1, 121–125. MR2902358 Snt ă m ă rian, Alina Some new sequences that converge to a generalized Euler constant. Appl. Math. Lett. 25 (2012), no. 6, 941–945. MR2902356 Wu, Xia ; Chen, Yanqiu Note on powers of 2 in sumsets. Appl. Math. Lett. 25 (2012), no. 6, 932–936. MR2902309 Dueez, E. ; Huynh, D. K. ; Keating, J. P. ; Miller, S. J. ; Snaith, N. C. A random matrix model for elliptic curve L -functions of finite conductor. J. Phys. 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MR2911143 Khan, Rizwanur Simultaneous non-vanishing of GL (3)× GL (2) and GL (2) L -functions. Math. Proc. Cambridge Philos. Soc. 152 (2012), no. 3, 535–553. MR2911139 Newton, Rachel Explicit local reciprocity for tame extensions. Math. Proc. Cambridge Philos. Soc. 152 (2012), no. 3, 425–454. MR2911138 Henriot, Kevin Nair-Tenenbaum bounds uniform with respect to the discriminant. Math. Proc. Cambridge Philos. Soc. 152 (2012), no. 3, 405–424. MR2911137 Sanders, Tom Approximate groups and doubling metrics. Math. Proc. Cambridge Philos. Soc. 152 (2012), no. 3, 385–404. MR2910780 Jeon, Daeyeol ; Kang, Soon-Yi ; Kim, Chang Heon Modularity of Galois traces of class invariants. Math. Ann. 353 (2012), no. 1, 37–63. MR2858937 Nguyen Quang Do, Thong Introduction à la Conjecture Principale de la théorie d'Iwasawa non commutative des corps totalement réels. (French) Actes de la Conférence "Fonctions L et Arithmétique'', 75–104, Publ. Math. Besanon Algèbre Théorie Nr., 2012/1, Presses Univ. Franche-Comté, Besanon, 2012. MR2858936 Greither, Cornelius Introduction à la conjecture ETNC et applications. (French) Actes de la Conférence "Fonctions L et Arithmétique'', 55–73, Publ. Math. Besanon Algèbre Théorie Nr., 2012/1, Presses Univ. Franche-Comté, Besanon, 2012. MR2858935 Bley, Werner La conjecture équivariante de Tamagawa. (French) Actes de la Conférence "Fonctions L et Arithmétique'', 27–53, Publ. Math. Besanon Algèbre Théorie Nr., 2012/1, Presses Univ. Franche-Comté, Besanon, 2012. MR2858934 Bencherif, Farid ; Garici, Tarek Suites de Cesàro et nombres de Bernoulli. (French) Actes de la Conférence "Fonctions L et Arithmétique'', 19–26, Publ. Math. Besanon Algèbre Théorie Nr., 2012/1, Presses Univ. Franche-Comté, Besanon, 2012. MR2858933 Asensouyis, Hassan ; Assim, Jilali Codescente pour le noyau sauvage étale. (French) Actes de la Conférence "Fonctions L et Arithmétique'', 5–17, Publ. Math. Besanon Algèbre Théorie Nr., 2012/1, Presses Univ. Franche-Comté, Besanon, 2012. MR2952081 Andrews, George E. ; Berndt, Bruce C. Ramanujan's lost notebook. Part III. Springer, New York, 2012. xii+435 pp. ISBN: 978-1-4614-3809-0 MR2910720 Kim, D. S. ; Kim, T. ; Dolgy, D. V. ; Lee, S. H. ; Rim, S.-H. Some properties and identities of Bernoulli and Euler polynomials associated with p -adic integral on Z p . Abstr. Appl. Anal. 2012, Art. ID 847901, 12 pp. MR2909919 Voloch, José Felipe Finite descent obstruction for curves over function fields. Bull. Braz. Math. Soc. (N.S.) 43 (2012), no. 1, 1–6. MR2909767 Taelman, Lenny A Herbrand-Ribet theorem for function fields. Invent. Math. 188 (2012), no. 2, 253–275. MR2908739 Kovi č , Jurij The arithmetic derivative and antiderivative. J. Integer Seq. 15 (2012), no. 3, Article 12.3.8, 16 pp. MR2012-08-333 for Number Theory.pdf
2012年4月份MR 题录数论最新文献246篇 ， http://blog.sciencenet.cn/blog-212210-568217.html 5月份MR题录数论最新研究文献311篇， http://blog.sciencenet.cn/blog-212210-577496.html 6月份MR题录数学文献15957篇，其中题录数论最新文献234篇，摘录部分内容如下，更多信息请浏览附件。 June 2012-Number theory.pdf MR2888757 Kendirli, Barış Letter to the editor: Cusp forms in S 4 ( Γ 0 ( 47 ) ) S\sb 4(\Gamma\sb 0(47)) and the number of representations of positive integers by some direct sum of binary quadratic forms with discriminant − 47 -47 . Int. J. Math. Math. Sci. 2012, Art. ID 303492, 10 pp. MR2888447 Koo, Ja Kyung ; Shin, Dong Hwa ; Yoon, Dong Sung Algebraic integers as special values of modular units. Proc. Edinb. Math. Soc. (2) 55 (2012), no. 1, 167–179. MR2888695 Pillichshammer, Friedrich A generalisation of a result of de la Vallée Poussin. Elem. Math. 67 (2012), no. 1, 26–38. MR2887894 Konstantinou, Elisavet ; Kontogeorgis, Aristides Ramanujan invariants for discriminants congruent to 5 ( mod 24 ) 5\pmod{24} . Int. J. Number Theory 8 (2012), no. 1, 265–287. MR2887893 Perucca, Antonella The multilinear support problem for products of abelian varieties and tori. Int. J. Number Theory 8 (2012), no. 1, 255–264. MR2887892 McGown, Kevin J. Norm-Euclidean cyclic fields of prime degree. Int. J. Number Theory 8 (2012), no. 1, 227–254. MR2887891 Sun, Zhi-Hong Identities and congruences for a new sequence. Int. J. Number Theory 8 (2012), no. 1, 207–225. MR2887890 Fukshansky, Lenny ; Petersen, Kathleen On well-rounded ideal lattices. Int. J. Number Theory 8 (2012), no. 1, 189–206. MR2887889 Noble, Rob Asymptotics of the weighted Delannoy numbers. Int. J. Number Theory 8 (2012), no. 1, 175–188. MR2887888 Filaseta, M. ; Laishram, S. ; Saradha, N. Solving n ( n + d ) ⋯ ( n + ( k − 1 ) d ) = b y 2 n(n+d)\cdots(n+(k-1)d)=by\sp 2 with P ( b ) ≤ C k P(b)\leq Ck . Int. J. Number Theory 8 (2012), no. 1, 161–173. MR2887887 Schweiger, F. A 2-dimensional algorithm related to the Farey-Brocot sequence. Int. J. Number Theory 8 (2012), no. 1, 149–160. MR2887886 Kadiri, Habiba Explicit zero-free regions for Dedekind zeta functions. Int. J. Number Theory 8 (2012), no. 1, 125–147. MR2887885 Chan, Song Heng ; Mao, Renrong Two congruences for Appell-Lerch sums. Int. J. Number Theory 8 (2012), no. 1, 111–123. MR2887884 Macias Castillo, Daniel On higher-order Stickelberger-type theorems for multi-quadratic extensions. Int. J. Number Theory 8 (2012), no. 1, 95–110. MR2887883 Amdeberhan, Tewodros ; Koutschan, Christoph ; Moll, Victor H. ; Rowland, Eric S. The iterated integrals of ln ( 1 + x n ) \ln(1+x\sp n) . Int. J. Number Theory 8 (2012), no. 1, 71–94. MR2887882 Akbary, Amir ; Ghioca, Dragos A geometric variant of Titchmarsh divisor problem. Int. J. Number Theory 8 (2012), no. 1, 53–69. MR2887881 Finotti, Luís R. A. Nonexistence of pseudo-canonical liftings. Int. J. Number Theory 8 (2012), no. 1, 31–51. MR2887873 Matomki, Kaisa On signs of Fourier coefficients of cusp forms. Math. Proc. Cambridge Philos. Soc. 152 (2012), no. 2, 207–222. MR2887111 Panzone, Pablo A. On the generating functions of Mersenne and Fermat primes. Collect. Math. 63 (2012), no. 1, 59–69. MR2886726 Haukkanen, Pentti A topological approach to divisibility of arithmetical functions and GCD matrices. Linear Multilinear Algebra 60 (2012), no. 3, 301–309. MR2886648 Jakubec, Stanislav A connection between sums of binomial coefficients and Gross-Koblitz formula. Math. Slovaca 62 (2012), no. 1, 13–16. MR2886617 Knill, Oliver ; Lesieutre, John Analytic continuation of Dirichlet series with almost periodic coefficients. Complex Anal. Oper. Theory 6 (2012), no. 1, 237–255. MR2886493 Deléglise, M. ; Nicolas, J.-L. Le plus grand facteur premier de la fonction de Landau. (French) Ramanujan J. 27 (2012), no. 1, 109–145. MR2886492 Furcy, David ; Penniston, David Congruences for ℓ \ell -regular partition functions modulo 3. Ramanujan J. 27 (2012), no. 1, 101–108. MR2886491 Ogasawara, Takeshi An eigenform of weight one expressed by meromorphic η \eta -quotients. Ramanujan J. 27 (2012), no. 1, 89–99. MR2886490 Haukkanen, Pentti ; Tóth, László An analogue of Ramanujan's sum with respect to regular integers ( mod r ) \pmod r . Ramanujan J. 27 (2012), no. 1, 71–88. MR2886489 Morgenbesser, Johannes F. The sum of digits of Gaussian primes. Ramanujan J. 27 (2012), no. 1, 43–70. MR2886488 Rubinstein, Michael O. Identities for the Riemann zeta function. Ramanujan J. 27 (2012), no. 1, 29–42. MR2886487 Takeyama, Yoshihiro Quadratic relations for a q q -analogue of multiple zeta values. Ramanujan J. 27 (2012), no. 1, 15–28. MR2886486 Gimenez, Jose ; Raji, Wissam q-expansions of vector-valued modular forms of negative weight. Ramanujan J. 27 (2012), no. 1, 1–13. MR2919246 De Koninck, Jean-Marie ; Luca, Florian Analytic number theory. Exploring the anatomy of integers. Graduate Studies in Mathematics, 134. American Mathematical Society, Providence, RI, 2012. xviii+414 pp. ISBN: 978-0-8218-7577-3 MR2919231 Clapperton, James A. ; Larcombe, Peter J. ; Fennessey, Eric J. The Delannoy numbers: three new non-linear identities. Bull. Inst. Combin. Appl. 64 (2012), 39–56. MR2919230 Eggleton, Roger B. ; Kimberley, Jason S. ; MacDougall, James A. Runs of integers with equally many distinct prime factors. Bull. Inst. Combin. Appl. 64 (2012), 30–38. MR2886499 lvarez, A. Annihilators for cusp forms of weight 2 and level 4 p m 4p\sp m . Ramanujan J. 27 (2012), no. 2, 209–227. MR2886498 Muić, Goran Modular curves and bases for the spaces of cuspidal modular forms. Ramanujan J. 27 (2012), no. 2, 181–208. MR2886497 Mortici, Cristinel Error estimates of Ramanujan-type series. Ramanujan J. 27 (2012), no. 2, 169–179. MR2886496 Keith, William J. A bijection for partitions with initial repetitions. Ramanujan J. 27 (2012), no. 2, 163–167. MR2886495 Amersi, Nadine ; Beyerl, Jeffrey ; Brown, Jim ; Proffer, Allison ; Rolen, Larry Pullbacks of Siegel Eisenstein series and weighted averages of critical L L -values. Ramanujan J. 27 (2012), no. 2, 151–162. MR2877978 Mortici, Cristinel A converse of a result about the floor function by Hermite. Internat. J. Math. Ed. Sci. Tech. 43 (2012), no. 1, 114–118. MR2877976 Koshy, Thomas Catalan's intriguing factorial problem. Internat. J. Math. Ed. Sci. Tech. 43 (2012), no. 1, 101–109. MR2905688 Wang, Tingting ; Tan, Qianrong ; Hong, Shaofang Arithmetic properties of a curious arithmetic function. Proceedings of the International Conference on Algebra 2010, 667–672, World Sci. Publ., Hackensack, NJ, 2012. MR2886211 Komornik, V. Unique infinite expansions in noninteger bases. Acta Math. Hungar. 134 (2012), no. 3, 344–355. MR2885985 Ru, Min ; Wang, Julie Tzu-Yueh An effective Schmidt's subspace theorem for projective varieties over function fields. Int. Math. Res. Not. 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5月份MR题录14097条，其中数论311条，摘录如下。由于对于数学表达式支持不够好，有些比较复杂的公式可能显示出现异常，建议读者浏览 http://www.ams.org/mathscinet/ MR2907327 Sahin, Murat ; Webb, William Conditional Lucas pseudoprimes. Ars Combin. 103 (2012), 129–136. MR2876337 Epifanio, C. ; Frougny, C. ; Gabriele, A. ; Mignosi, F. ; Shallit, J. Sturmian graphs and integer representations over numeration systems. Discrete Appl. Math. 160 (2012), no. 4-5, 536–547. MR2876388 Brown, David Primitive integral solutions to x 2 + y 3 = z 10 x\sp 2+y\sp 3=z\sp {10} . Int. Math. Res. Not. IMRN 2012, no. 2, 423–436. MR2876385 Galateau, Aurélien Petits points des hypersurfaces d'une variété abélienne. (French) Int. Math. Res. Not. IMRN 2012, no. 2, 339–359. MR2907541 Bae, Sunghan ; Jung, Hwanyup ℓ \ell -ranks of class groups of function fields. J. Korean Math. Soc. 49 (2012), no. 1, 49–67. MR2876275 Li, Taiyu On sums of squares of primes and a k k th power of prime. Rocky Mountain J. Math. 42 (2012), no. 1, 201–222. MR2876270 Hambleton, S. ; Scharaschkin, V. 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Algebra 216 (2012), no. 5, 1184–1195. Publications results for "All publications entered last month AND classification = (11)" MR2873106 Christopoulou, M. ; Garefalakis, T. ; Panario, D. ; Thomson, D. Gauss periods as constructions of low complexity normal bases. Des. Codes Cryptogr. 62 (2012), no. 1, 43–62. MR2874963 Masser, D. ; Zannier, U. Torsion points on families of squares of elliptic curves. Math. Ann. 352 (2012), no. 2, 453–484. MR2874930 Ganguly, Satadal ; Sengupta, Jyoti Sums of Kloosterman sums over arithmetic progressions. Int. Math. Res. Not. IMRN 2012, no. 1, 137–165. MR2874929 McKee, James ; Smyth, Chris Integer symmetric matrices of small spectral radius and small Mahler measure. Int. Math. Res. Not. IMRN 2012, no. 1, 102–136. MR2874918 Gurevich, Alexander ; Kunyavskiĭ, Boris Deterministic primality tests based on tori and elliptic curves. Finite Fields Appl. 18 (2012), no. 1, 222–236. MR2874916 Zhu, Guizhen ; Wan, Daqing An asymptotic formula for counting subset sums over subgroups of finite fields. Finite Fields Appl. 18 (2012), no. 1, 192–209. MR2874915 Meemark, Yotsanan ; Wiroonsri, Nathakhun The digraph of the k k th power mapping of the quotient ring of polynomials over finite fields. Finite Fields Appl. 18 (2012), no. 1, 179–191. MR2874913 Gloğlu, F. Ternary Kloosterman sums modulo 4. Finite Fields Appl. 18 (2012), no. 1, 160–166. MR2874909 Stichtenoth, Henning ; Topuzoğlu, Alev Factorization of a class of polynomials over finite fields. Finite Fields Appl. 18 (2012), no. 1, 108–122. MR2874905 Ling, San ; Qu, Longjiang A note on linearized polynomials and the dimension of their kernels. Finite Fields Appl. 18 (2012), no. 1, 56–62. MR2874904 Zhao, Xiaomei A note on multiple exponential sums in function fields. Finite Fields Appl. 18 (2012), no. 1, 35–55. MR2874903 Lasjaunias, A. On the continued fraction expansion of the unique root in F ( p ) \Bbb F(p) of the equation x 4 + x 2 − T x − 1 / 12 = 0 x\sp 4+x\sp 2-Tx-1/12=0 and other related hyperquadratic expansions. Finite Fields Appl. 18 (2012), no. 1, 26–34. MR2874902 Bayad, Abdelmejid ; Hamahata, Yoshinori Higher dimensional Dedekind sums in finite fields. Finite Fields Appl. 18 (2012), no. 1, 19–25. MR2874897 Büyükboduk, Kzim Height pairings, exceptional zeros and Rubin's formula: the multiplicative group. Comment. Math. Helv. 87 (2012), no. 1, 71–111. MR2874646 Taelman, Lenny Special L L -values of Drinfeld modules. Ann. of Math. (2) 175 (2012), no. 1, 369–391. MR2874644 de la Bretèche, Régis ; Browning, Tim ; Peyre, Emmanuel On Manin's conjecture for a family of Chtelet surfaces. Ann. of Math. (2) 175 (2012), no. 1, 297–343. MR2874641 Beresnevich, Victor Rational points near manifolds and metric Diophantine approximation. Ann. of Math. (2) 175 (2012), no. 1, 187–235. MR2873803 Fried, Michael D. Variables separated equations: strikingly different roles for the branch cycle lemma and the finite simple group classification. Sci. China Math. 55 (2012), no. 1, 1–72. MR2873092 Wenpeng, Zhang ; Tingting, Wang The infinite sum of reciprocal Pell numbers. Appl. Math. Comput. 218 (2012), no. 10, 6164–6167. MR2873083 Yaşar, Meral ; Bozkurt, Durmuş Another proof of Pell identities by using the determinant of tridiagonal matrix. Appl. Math. Comput. 218 (2012), no. 10, 6067–6071. MR2872923 Gyarmati, Katalin ; Mauduit, Christian On the correlation of binary sequences, II. Discrete Math. 312 (2012), no. 5, 811–818. MR2872554 Pierce, Lillian B. Discrete fractional Radon transforms and quadratic forms. Duke Math. J. 161 (2012), no. 1, 69–106. MR2872485 Alexandru, V. ; Popescu, N. ; Vjitu, M. ; Zaharescu, A. Representation results for equivariant rigid analytic functions. Algebr. Represent. Theory 15 (2012), no. 1, 137–145. 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(French) Acta Arith. 152 (2012), no. 2, 185–216. MR2864392 Kikuta, Toshiyuki On p -adic Siegel modular forms of non-real Nebentypus. Acta Arith. 152 (2012), no. 2, 175–183. MR2864391 Arai, Keisuke ; Momose, Fumiyuki Points on X + 0 ( N ) over quadratic fields. Acta Arith. 152 (2012), no. 2, 159–173. MR2864390 Liu, Huaning ; Zhai, Wenguang The equation n 1 n 2 = n 3 n 4 , the gcd-sum function and the mean values of certain character sums. Acta Arith. 152 (2012), no. 2, 137–157. MR2864389 Katsurada, Masanori Complete asymptotic expansions for certain multiple q -integrals and q -differentials of Thomae-Jackson type. Acta Arith. 152 (2012), no. 2, 109–136. MR2789663 Ralph, Claire C. ; Simanca, Santiago R. Arithmetic differential operators over the p -adic integers. London Mathematical Society Lecture Note Series, 396. Cambridge University Press, Cambridge, 2012. vi+139 pp. ISBN: 978-1-107-67414-1 MR2896582 Le Gonidec, Marion On the complexity of a family of k -context-free sequences. Theoret. Comput. Sci. 414 (2012), 47–54. MR2872210 Ichimura, Humio ; Nakajima, Shoichi A note on the relative class number of the cyclotomic Z p -extension of Q ( − p − − − ? ) . Proc. Japan Acad. Ser. A Math. Sci. 88 (2012), no. 1, 16–20. MR2872209 Choi, Soyoung p -adic properties of coefficients of basis for the space of weakly holomorphic modular forms of weight 2. Proc. Japan Acad. Ser. A Math. Sci. 88 (2012), no. 1, 11 –15. MR2871754 Aschenbrenner, Matthias Logarithms of iteration matrices, and proof of a conjecture by Shadrin and Zvonkine. J. Combin. Theory Ser. A 119 (2012), no. 3, 627–654. MR2871150 Folsom, Amanda ; Kent, Zachary A. ; Ono, Ken ℓ -adic properties of the partition function. Appendix A by Nick Ramsey. Adv. Math. 229 (2012), no. 3, 1586–1609. MR2869141 Hoffman, Jerome William ; Long, Ling ; Verrill, Helena On ℓ -adic representations for a space of noncongruence cuspforms. Proc. Amer. Math. Soc. 140 (2012), no. 5, 1569–1584. 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2012年5月上旬， MRDB数据库（ http://www.ams.org/mathscinet/index.html ） 收录的数论最新文献117篇，其题录如下： 如果其中有些数学关系式显示出现差错，可以点击前面MR文摘号，即可链接到MRDB，详细阅读原文（注意可能需要注册或者必须是包库用户方可使用）。原文获取方法有多种，通过搜索引擎进行搜索就是一个很好的选择，也可以直接与作者联系，一般作者均有电子文档。 MR2905431 Morishita, Masanori Knots and primes. An introduction to arithmetic topology. Universitext. Springer, London, 2012. xii+191 pp. ISBN: 978-1-4471-2157-2 MR2869202 Gonek, S. M. Finite Euler products and the Riemann hypothesis. Trans. Amer. Math. Soc. 364 (2012), no. 4, 2157–2191. MR2869201 Akhtari, Shabnam Representation of unity by binary forms. Trans. Amer. Math. Soc. 364 (2012), no. 4, 2129–2155. MR2869105 Shparlinski, Igor E. On the value set of Fermat quotients. Proc. Amer. Math. Soc. 140 (2012), no. 4, 1199–1206. MR2869098 Kohnen, Winfried ; Mason, Geoffrey On the canonical decomposition of generalized modular functions. Proc. Amer. Math. Soc. 140 (2012), no. 4, 1125–1132. MR2869321 Couveignes, Jean-Marc ; Kammerer, Jean-Gabriel The geometry of flex tangents to a cubic curve and its parameterizations. J. Symbolic Comput. 47 (2012), no. 3, 266–281. MR2869212 Strmbergsson, Andreas On the limit distribution of Frobenius numbers. Acta Arith. 152 (2012), no. 1, 81–107. MR2869211 Bayad, Abdelmejid ; Hamahata, Yoshinori Higher dimensional Dedekind sums in function fields. Acta Arith. 152 (2012), no. 1, 71–80. MR2869210 de Jong, Robin Local heights on Galois covers of the projective line. Acta Arith. 152 (2012), no. 1, 51–70. MR2869209 Schoof, René ; Tzanakis, Nikos Integral points of a modular curve of level 11 . Acta Arith. 152 (2012), no. 1, 39–49. MR2869208 Chang, Mei-Chu Short character sums with Fermat quotients. Acta Arith. 152 (2012), no. 1, 23–38. MR2869207 Ito, Hiroshi A note on a product formula for the cubic Gauss sum. Acta Arith. 152 (2012), no. 1, 11 –21. MR2869206 Chan, T. H. ; Kumchev, A. V. On sums of Ramanujan sums. Acta Arith. 152 (2012), no. 1, 1–10. MR2869064 Languasco, Alessandro ; Zaccagnini, Alessandro The number of Goldbach representations of an integer. Proc. Amer. Math. Soc. 140 (2012), no. 3, 795–804. MR2869060 Fukuyama, Katusi ; Watada, Tetsujin A metric discrepancy result for lacunary sequences. Proc. Amer. Math. Soc. 140 (2012), no. 3, 749–754. MR2869058 Tao, Terence ; Croot, Ernest, III ; Helfgott, Harald Deterministic methods to find primes. Math. Comp. 81 (2012), no. 278, 1233–1246. MR2869057 Brker, Reinier ; Lauter, Kristin ; Sutherland, Andrew V. Modular polynomials via isogeny volcanoes. Math. Comp. 81 (2012), no. 278, 1201–1231. MR2869056 Loeffler, David ; Weinstein, Jared On the computation of local components of a newform. Math. Comp. 81 (2012), no. 278, 1179–1200. MR2869053 Sutherland, Andrew V. Constructing elliptic curves over finite fields with prescribed torsion. Math. Comp. 81 (2012), no. 278, 1131–1147. MR2869052 Heijne, Bas The maximal rank of elliptic Delsarte surfaces. Math. Comp. 81 (2012), no. 278, 1111–1130. MR2869051 Jiménez Urroz, Jorge ; Luca, Florian ; Shparlinski, Igor E. On the number of isogeny classes of pairing-friendly elliptic curves and statistics of MNT curves. Math. Comp. 81 (2012), no. 278, 1093–1110. MR2869050 Keller, Wolfgang ; Martinet, Jacques ; Schürmann, Achill On classifying Minkowskian sublattices. With an appendix by Mathieu Dutour Sikirić. Math. Comp. 81 (2012), no. 278, 1063–1092. MR2869049 Trudgian, Timothy An improved upper bound for the argument of the Riemann zeta-function on the critical line. Math. Comp. 81 (2012), no. 278, 1053–1061. MR2869048 Berkane, D. ; Bordellès, O. ; Ramaré, O. Explicit upper bounds for the remainder term in the divisor problem. Math. Comp. 81 (2012), no. 278, 1025–1051. MR2869047 Chen, William Y. C. ; Fan, Neil J. Y. ; Jia, Jeffrey Y. T. The generating function for the Dirichlet series $L\sb {m}(s)$ L m ( s ) L\sb {m}(s) . Math. Comp. 81 (2012), no. 278, 1005–1023. MR2869029 Marshall, Simon Erratum to "Mass equidistribution for automorphic forms of cohomological type on $GL\sb {2}$ G L 2 GL\sb {2} '' . J. Amer. Math. Soc. 25 (2012), no. 2, 615–616. MR2869028 Bateman, Michael ; Katz, Nets Hawk New bounds on cap sets. J. Amer. Math. Soc. 25 (2012), no. 2, 585–613. MR2869026 Calegari, Frank Even Galois representations and the Fontaine–Mazur conjecture. II. J. Amer. Math. Soc. 25 (2012), no. 2, 533–554. MR2869024 Miller, Stephen D. ; Schmid, Wilfried The Archimedean theory of the exterior square $L$ L L -functions over $\Bbb{Q}$ Q \Bbb{Q} . J. Amer. Math. Soc. 25 (2012), no. 2, 465–506. MR2869007 Scanlon, Thomas Counting special points: Logic, diophantine geometry, and transcendence theory. Bull. Amer. Math. Soc. (N.S.) 49 (2012), no. 1, 51–71. MR2869006 Nadler, David The geometric nature of the fundamental lemma. Bull. Amer. Math. Soc. (N.S.) 49 (2012), no. 1, 1–50. MR2864867 Enriquez, Benjamin ; Furusho, Hidekazu Mixed pentagon, octagon, and Broadhurst duality equations. J. Pure Appl. Algebra 216 (2012), no. 4, 982–995. MR2862374 Hindry, Marc ; Ratazzi, Nicolas Points de torsion sur les variétés abéliennes de type GSp. (French) J. Inst. Math. Jussieu 11 (2012), no. 1, 27–65. MR2864426 Lladó, Anna ; Moragas, Jordi On the modular sumset partition problem. European J. Combin. 33 (2012), no. 4, 427–434. MR2863812 Cai, Y.-C. ; Lu, M.-G. On the slim exceptional set for the Lagrange four squares theorem. Acta Math. Hungar. 134 (2012), no. 1-2, 115–131. MR2863809 Huang, J. A mean value theorem for the Diophantine equation $axy-x-y=n$ a x y − x − y = n axy-x-y=n . Acta Math. Hungar. 134 (2012), no. 1-2, 68–78. MR2863805 Nowak, W. G. Higher order derivative tests for exponential sums incorporating the discrete Hardy-Littlewood method. Acta Math. Hungar. 134 (2012), no. 1-2, 12–28. MR2863752 García-Selfa, Irene ; Tornero, José M. A complete Diophantine characterization of the rational torsion of an elliptic curve. Acta Math. Sin. (Engl. Ser.) 28 (2012), no. 1, 83–96. MR2861775 Fukuhara, Shinji A basis for the space of modular forms. Acta Arith. 151 (2012), no. 4, 421–427. MR2861774 Saradha, N. Application of the explicit $abc$ a b c abc -conjecture to two Diophantine equations. Acta Arith. 151 (2012), no. 4, 401–419. MR2861773 Lee, Siu-lun Alan On Waring's problem: two cubes and two minicubes. Acta Arith. 151 (2012), no. 4, 377–399. MR2861772 Bedratyuk, Leonid Semi-invariants of binary forms and identities for Bernoulli, Euler and Hermite polynomials. Acta Arith. 151 (2012), no. 4, 361–376. MR2861771 Bae, Sunghan ; Jung, Hwanyup On the 4-rank of ideal class groups of quadratic function fields. Acta Arith. 151 (2012), no. 4, 325–360. MR2895235 Aurich, Ralf ; Steiner, Frank ; Then, Holger Numerical computation of Maass waveforms and an application to cosmology. Hyperbolic geometry and applications in quantum chaos and cosmology, 229–269, London Math. Soc. Lecture Note Ser., 397, Cambridge Univ. Press, Cambridge, 2012. MR2895234 Strmberg, Fredrik Maass waveforms on $(\Gamma\sb 0(N),\chi)$ ( Γ 0 ( N ) , χ ) (\Gamma\sb 0(N),\chi) (computational aspects). Hyperbolic geometry and applications in quantum chaos and cosmology, 187–228, London Math. Soc. Lecture Note Ser., 397, Cambridge Univ. Press, Cambridge, 2012. MR2895233 Hejhal, Dennis A. On the calculation of Maass cusp forms. Hyperbolic geometry and applications in quantum chaos and cosmology, 175–185, London Math. Soc. Lecture Note Ser., 397, Cambridge Univ. Press, Cambridge, 2012. MR2885182 Marklof, Jens Selberg's trace formula: an introduction. Hyperbolic geometry and applications in quantum chaos and cosmology, 83–119, London Math. Soc. Lecture Note Ser., 397, Cambridge Univ. Press, Cambridge, 2012. MR2864372 Erdélyi, Tamás ; Khodjasteh, Kaveh ; Viola, Lorenza The size of exponential sums on intervals of the real line. Constr. Approx. 35 (2012), no. 1, 123–136. MR2863489 Eliahou, S. ; Marín, J. M. ; Revuelta, M. P. ; Sanz, M. I. Weak Schur numbers and the search for G. W. Walker's lost partitions. Comput. Math. Appl. 63 (2012), no. 1, 175–182. MR2863474 Yazlik, Yasin ; Taskara, Necati A note on generalized $k$ k k -Horadam sequence. Comput. Math. Appl. 63 (2012), no. 1, 36–41. MR2896066 Keke, Gülcan On the values of some generalized lacunary power series with algebraic coefficients for Liouville number arguments. Hacet. J. Math. Stat. 40 (2011), no. 5, 691–702. MR2871317 Dąbrowski, Andrzej On the Lebesgue-Nagell equation. Colloq. Math. 125 (2011), no. 2, 245–253. MR2905408 Somer, Lawrence ; Křížek, Michal The structure of digraphs associated with the congruence $x\sp k\equiv y\pmod n$ x k ≡ y ( m o d n ) x\sp k\equiv y\pmod n . Czechoslovak Math. J. 61(136) (2011), no. 2, 337–358. MR2895875 Lemma, Mulatu The Mulatu numbers. Adv. Appl. Math. Sci. 10 (2011), no. 4, 431–440. MR2895332 González, Josep Finiteness of endomorphism algebras of CM modular abelian varieties. Rev. Mat. Iberoam. 27 (2011), no. 3, 733–750. MR2895319 Moon, Hyunsuk On the structure of the Mordell-Weil groups of the Jacobians of curves defined by $y\sp n=f(x)$ y n = f ( x ) y\sp n=f(x) . Math. J. Okayama Univ. 54 (2011), 49–52. MR2895318 Ichimura, Humio Hilbert-Speiser number fields and Stickelberger ideals: the case $p=2$ p = 2 p=2 . Math. J. Okayama Univ. 54 (2011), 33–48. MR2895317 Suwa, Noriyuki Some remarks on Lucas pseudoprimes. Math. J. Okayama Univ. 54 (2011), 1–32. MR2895177 Park, Hwasin ; Kim, Aeran ; Kim, Daeyeoul ; Kim, Minhee Elliptic curves with the real $\wp$ ℘ \wp -function. JP J. Algebra Number Theory Appl. 23 (2011), no. 2, 249–255. MR2894627 Caragiu, Mihai ; Sutherland, Lauren ; Zaki, Mohammad Multidimensional greatest prime factor sequences. JP J. Algebra Number Theory Appl. 23 (2011), no. 2, 187–195. MR2894626 Rault, Patrick X. On uniform bounds for rational points on rational curves and thin sets. JP J. Algebra Number Theory Appl. 23 (2011), no. 2, 171–185. MR2894625 Gauthier, Claude Solving nonlinear Diophantine equations through inequalities between rational numbers. JP J. Algebra Number Theory Appl. 23 (2011), no. 2, 165–170. MR2870099 Brker, Reinier ; Gruenewald, David ; Lauter, Kristin Explicit CM theory for level 2-structures on abelian surfaces. Algebra Number Theory 5 (2011), no. 4, 495–528. MR2870098 Ingram, Patrick Specializations of elliptic surfaces, and divisibility in the Mordell-Weil group. Algebra Number Theory 5 (2011), no. 4, 465–493. MR2870097 Couveignes, Jean-Marc ; Hallouin, Emmanuel Global descent obstructions for varieties. Algebra Number Theory 5 (2011), no. 4, 431–463. MR2869849 Ustinov, A. V. On Voronoĭ's theorem on cylindrical minima of three-dimensional lattices. (Russian) Dalʹnevost. Mat. Zh. 11 (2011), no. 2, 213–221. MR2869844 Illarionov, A. A. ; Soĭka, Yu. A. On the number of relative minima of integer lattices. (Russian) Dalʹnevost. Mat. Zh. 11 (2011), no. 2, 149–154. MR2869438 Markin, Nadya ; Ullom, Stephen V. Minimal ramification in nilpotent extensions. Pacific J. Math. 253 (2011), no. 1, 125–143. MR2869308 Matomki, Kaisa A note on signs of Kloosterman sums. Bull. Soc. Math. France 139 (2011), no. 3, 287–295. MR2869306 de La Rochefoucauld, Thomas Invariance of the parity conjecture for $p$ p p -Selmer groups of elliptic curves in a $D\sb {2p\sp n}$ D 2 p n D\sb {2p\sp n} -extension. Bull. Soc. Math. France 139 (2011), no. 4, 571–592. MR2869300 Lafforgue, Vincent Estimées pour les valuations $p$ p p -adiques des valeurs propes des opérateurs de Hecke. (French) Bull. Soc. Math. France 139 (2011), no. 4, 455–477. MR2869299 Corvaja, Pietro ; Zannier, Umberto An $abcd$ a b c d abcd theorem over function fields and applications. Bull. Soc. Math. France 139 (2011), no. 4, 437–454. MR2863371 Benois, Denis A generalization of Greenberg's $\scr L$ L \scr L -invariant. Amer. J. Math. 133 (2011), no. 6, 1573–1632. MR2863370 Nguyen Quang Do, Thong ; Nicolas, Vésale Nombres de Weil, sommes de Gauss et annulateurs galoisiens. (French) Amer. J. Math. 133 (2011), no. 6, 1533–1571. MR2896405 Jolany, Hassan ; Eizadi Alikelaye, R. ; Sharif Mohamad, Shangil Some results on the generalization of Bernoulli, Euler and Genocchi polynomials. Acta Univ. Apulensis Math. Inform. No. 27 (2011), 299–306. MR2895468 Saikia, Manjil P. ; Vogrinc, Jure Binomial symbols and prime moduli. J. Indian Math. Soc. (N.S.) 78 (2011), no. 1-4, 137–143. MR2861943 Kim, Dae San ; Kim, Taekyun ; Lee, Sang-Hun ; Dolgy, D. V. ; Rim, Seog-Hoon Some new identities on the Bernoulli and Euler numbers. Discrete Dyn. Nat. Soc. 2011, Art. ID 856132, 11 pp. MR2861941 Kılı, E. ; mür, N. ; Ulutaş, Y. T. Some finite sums involving generalized Fibonacci and Lucas numbers. Discrete Dyn. Nat. Soc. 2011, Art. ID 284261, 11 pp. MR2861083 Wakayama, Masato ; Yamasaki, Yoshinori Higher regularizations of zeros of cuspidal automorphic $L$ L L -functions of ${\rm GL}\sb d$ G L d {\rm GL}\sb d . J. Théor. Nombres Bordeaux 23 (2011), no. 3, 751–767. MR2861082 Ordaz, Oscar ; Philipp, Andreas ; Santos, Irene ; Schmid, Wolfgang A. On the Olson and the strong Davenport constants. J. Théor. Nombres Bordeaux 23 (2011), no. 3, 715–750. MR2861081 Luca, Florian ; Pollack, Paul An arithmetic function arising from Carmichael's conjecture. J. Théor. Nombres Bordeaux 23 (2011), no. 3, 697–714. MR2861080 Guàrdia, Jordi ; Montes, Jesús ; Nart, Enric Higher Newton polygons in the computation of discriminants and prime ideal decomposition in number fields. J. Théor. Nombres Bordeaux 23 (2011), no. 3, 667–696. MR2861077 Centeleghe, Tommaso Giorgio Computing the number of certain Galois representations mod $p$ p p . J. Théor. Nombres Bordeaux 23 (2011), no. 3, 603–627. MR2861076 Browning, Tim The divisor problem for binary cubic forms. J. Théor. Nombres Bordeaux 23 (2011), no. 3, 579–602. MR2861075 Berthomieu, Jérémy ; Van Der Hoeven, Joris ; Lecerf, Grégoire Relaxed algorithms for $p$ p p -adic numbers. J. Théor. Nombres Bordeaux 23 (2011), no. 3, 541–577. MR2861074 Adam, Brigitte ; Rhin, Georges Periodic Jacobi-Perron expansions associated with a unit. J. Théor. Nombres Bordeaux 23 (2011), no. 3, 527–539. MR2896168 Illarionov, A. A. The average number of relative minima of three-dimensional integer lattices. (Russian) Algebra i Analiz 23 (2011), no. 3, 189–215. MR2896164 Budarina, N. V. On primitively 2-universal quadratic forms. (Russian) Algebra i Analiz 23 (2011), no. 3, 31–62. MR2882402 Shamseddine, Khodr Absolute and relative extrema, the mean value theorem and the inverse function theorem for analytic functions on a Levi-Civita field. Advances in non-Archimedean analysis, 257–268, Contemp. Math., 551, Amer. Math. Soc., Providence, RI, 2011. MR2882398 Maga, Hamadoun Identities and congruences for Genocchi numbers. Advances in non-Archimedean analysis, 207–220, Contemp. Math., 551, Amer. Math. Soc., Providence, RI, 2011. MR2861691 Miller, Robert L. Proving the Birch and Swinnerton-Dyer conjecture for specific elliptic curves of analytic rank zero and one. LMS J. Comput. Math. 14 (2011), 327–350. MR2861596 Liu, Jianya Integral points on quadrics with prime coordinates. Monatsh. Math. 164 (2011), no. 4, 439–465. MR2868578 Yoshida, Manabu Ramification of local fields and Fontaine's property $({\rm P}\sb m)$ ( P m ) ({\rm P}\sb m) : a résumé. Algebraic number theory and related topics 2009, 255–258, RIMS Kkyroku Bessatsu, B25, Res. Inst. Math. Sci. (RIMS), Kyoto, 2011. MR2868577 Taniguchi, Takashi An introduction to higher composition laws. (Japanese) Algebraic number theory and related topics 2009, 211–253, RIMS Kkyroku Bessatsu, B25, Res. Inst. Math. Sci. (RIMS), Kyoto, 2011. MR2868575 Nakamura, Kentaro Zariski density of two dimensional crystalline representations. (Japanese) Algebraic number theory and related topics 2009, 161–183, RIMS Kkyroku Bessatsu, B25, Res. Inst. Math. Sci. (RIMS), Kyoto, 2011. MR2868574 Miyake, Katsuya Takagi's class field theory—from where? and to where?—. Algebraic number theory and related topics 2009, 125–160, RIMS Kkyroku Bessatsu, B25, Res. Inst. Math. Sci. (RIMS), Kyoto, 2011. MR2868572 Fujii, Satoshi Greenberg's generalized conjecture and unramified Galois groups over the cyclotomic $\Bbb Z\sb p$ Z p \Bbb Z\sb p -extensions. Algebraic number theory and related topics 2009, 95–101, RIMS Kkyroku Bessatsu, B25, Res. Inst. Math. Sci. (RIMS), Kyoto, 2011. MR2868571 Ozeki, Yoshiyasu Non-existence of certain Galois representations with a uniform tame inertia weight: a resume. Algebraic number theory and related topics 2009, 89–92, RIMS Kkyroku Bessatsu, B25, Res. Inst. Math. Sci. (RIMS), Kyoto, 2011. MR2868568 Kashio, Tomokazu On a relation between $p$ p p -adic multiple gamma functions and $p$ p p -adic periods. (Japanese) Algebraic number theory and related topics 2009, 31–51, RIMS Kkyroku Bessatsu, B25, Res. Inst. Math. Sci. (RIMS), Kyoto, 2011. MR2868566 Algebraic number theory and related topics 2009. Papers from the RIMS Workshop held at Kyoto University, Kyoto, December 7– 11 , 2009. Edited by Takashi Ichikawa, Masanari Kida and Takao Yamazaki. RIMS Kkyroku Bessatsu , B25. Research Institute for Mathematical Sciences (RIMS), Kyoto, 2011. 258 pp. MR2863902 Flach, Matthias On the cyclotomic main conjecture for the prime 2. J. Reine Angew. Math. 661 (2011), 1–36. MR2863413 Nguyen, Viet Kh. On certain extremal pencils of curves with respect to the total reducibility order. Proc. Japan Acad. Ser. A Math. Sci. 87 (2011), no. 10, 194–198. MR2863410 Shiomi, Daisuke Determinant formulas for zeta functions for real abelian function fields. Proc. Japan Acad. Ser. A Math. Sci. 87 (2011), no. 10, 183–185. MR2862611 Mahadeva Naika, M. S. ; Chandankumar, S. ; Manjunatha, M. On some new modular equations and their applications to continued fractions. Int. Math. Forum 6 (2011), no. 57-60, 2881–2905. MR2862598 Jakimczuk, Rafael Functions of slow increase, integer sequences and conjectures. Int. Math. Forum 6 (2011), no. 53-56, 2703–2709. MR2863844 Šiaulys, Jonas ; Stepanauskas, Gediminas Binomial limit law for additive prime indicators. Lith. Math. J. 51 (2011), no. 4, 562–572. MR2863843 Pi, Qinghua Determination of cusp forms by central values of Rankin-Selberg $L$ L L -functions. Lith. Math. J. 51 (2011), no. 4, 543–561. MR2863839 Duy, Trinh Khanh Limit-periodic arithmetical functions and the ring of finite integral adeles. Lith. Math. J. 51 (2011), no. 4, 486–506. MR2863836 Budarina, Natalia Simultaneous Diophantine approximation in the real and $p$ p p -adic fields with nonmonotonic error function. Lith. Math. J. 51 (2011), no. 4, 461–471. MR2863357 Ito, Akiko A note on the divisibility of class numbers of imaginary quadratic fields $\bold Q(\sqrt{a\sp 2-k\sp n})$ Q ( a 2 − k n − − − − − − √ ) \bold Q(\sqrt{a\sp 2-k\sp n}) . Proc. Japan Acad. Ser. A Math. Sci. 87 (2011), no. 9, 151–155. MR2863194 Kedlaya, Kiran S. ; Umans, Christopher Fast polynomial factorization and modular composition. SIAM J. Comput. 40 (2011), no. 6, 1767–1802. MR2862575 Salas, Alvaro H. About $k$ k k -Fibonacci numbers and their associated numbers. Int. Math. Forum 6 (2011), no. 49-52, 2473–2479. MR2830739 Golomb, Solomon W. Infinite sequences with finite cross-correlation. Sequences and their applications—SETA 2010, 430–441, Lecture Notes in Comput. Sci., 6338, Springer, Berlin, 2010. MR2830724 Gloğlu, Faruk ; McGuire, Gary ; Moloney, Richard Ternary Kloosterman sums modulo 18 using Stickelberger's theorem. Sequences and their applications—SETA 2010, 196–203, Lecture Notes in Comput. Sci., 6338, Springer, Berlin, 2010. MR2830723 Gomez, Domingo Multiplicative character sums with counter-dependent nonlinear congruential pseudorandom number generators. Sequences and their applications—SETA 2010, 188–195, Lecture Notes in Comput. Sci., 6338, Springer, Berlin, 2010. MR2830718 eşmelioğlu, Aya ; Meidl, Wilfried A general approach to construction and determination of the linear complexity of sequences based on cosets. Sequences and their applications—SETA 2010, 125–138, Lecture Notes in Comput. Sci., 6338, Springer, Berlin, 2010. MR2836234 van der Geer, Gerard Hunting for curves with many points. Coding and cryptology, 82–96, Lecture Notes in Comput. 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对于美国《数学评论》数据库（MRDB）2011年11月到2012年3月的数论研究文献题录已有报道（ http://blog.sciencenet.cn/blog-212210-562076.html ），现在对于2012年4月MRDB题录的最新文献9984条中数论类文献246篇摘录如下，以供参考。其中有些数学关系式显示可能会出现差错，但是点击前面MR文摘号，即可链接到MRDB，详细阅读原文（注意可能需要注册或者必须是包库用户方可使用）。 MR2862037 Fuchs, Clemens ; Zannier, Umberto Composite rational functions expressible with few terms. J. Eur. Math. Soc. (JEMS) 14 (2012), no. 1, 175–208. MR2894618 Ash, Avner ; Gross, Robert Elliptic tales. Curves, counting, and number theory. Princeton University Press, Princeton, NJ, 2012. xxii+253 pp. ISBN: 978-0-691-15119-9 MR2862393 Zhang, Wenpeng A mean value related to D. H. Lehmer's problem and the Ramanujan's sum. Glasg. Math. J. 54 (2012), no. 1, 155–162. MR2862392 Zhu, Minhui ; Wang, Tingting The divisibility of the class number of the imaginary quadratic field $\bold Q(\sqrt{2\sp {2m}-k\sp n})$ Q ( 2 2 m − k n − − − − − − − √ ) \bold Q(\sqrt{2\sp {2m}-k\sp n}) . Glasg. Math. J. 54 (2012), no. 1, 149–154. MR2862391 Furuya, Jun ; Tanigawa, Yoshio Explicit representations of the integral containing the error term in the divisor problem II. Glasg. Math. J. 54 (2012), no. 1, 133–147. MR2862390 Zaimi, Toufik On the spectra of Pisot numbers. Glasg. Math. J. 54 (2012), no. 1, 127–132. MR2862389 Kim, Taekyun Note on $q$ q q -Dedekind-type sums related to $q$ q q -Euler polynomials. Glasg. Math. J. 54 (2012), no. 1, 121–125. MR2862320 Le Boudec, Pierre Power-free values of the polynomial $t\sb 1\cdots t\sb r-1$ t 1 ⋯ t r − 1 t\sb 1\cdots t\sb r-1 . Bull. Aust. Math. Soc. 85 (2012), no. 1, 154–163. MR2862315 Shen, Zhongyan ; Cai, Tianxin Rational points on three superelliptic curves. Bull. Aust. Math. Soc. 85 (2012), no. 1, 105–113. MR2862313 Yang, Quan-Hui ; Chen, Yong-Gao Sumsets and difference sets containing a common term of a sequence. Bull. Aust. Math. Soc. 85 (2012), no. 1, 79–83. MR2862306 Kim, Ji Young ; Lee, Young Min Sums of distinct integral squares in $\Bbb Q(\sqrt 2)$ Q ( 2 √ ) \Bbb Q(\sqrt 2) , $\Bbb Q(\sqrt 3)$ Q ( 3 √ ) \Bbb Q(\sqrt 3) and $\Bbb Q(\sqrt 6)$ Q ( 6 √ ) \Bbb Q(\sqrt 6) . Bull. Aust. Math. Soc. 85 (2012), no. 1, 1–10. MR2894984 Hida, Haruzo Geometric modular forms and elliptic curves. Second edition. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2012. xiv+454 pp. ISBN: 978-981-4368-64-3; 981-4368-64-4 MR2856019 Bazsó, A. ; Pintér, . ; Srivastava, H. M. A refinement of Faulhaber's theorem concerning sums of powers of natural numbers. Appl. Math. Lett. 25 (2012), no. 3, 486–489. MR2855982 Chen, Chao-Ping ; Srivastava, H. M. New representations for the Lugo and Euler-Mascheroni constants. II. Appl. Math. Lett. 25 (2012), no. 3, 333–338. MR2860957 Pong, Wai Yan ; Stroeker, Roelof J. Diophantine equations of matching games II. Acta Arith. 151 (2012), no. 3, 311–323. 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Linear forms and quadratic uniformity for functions on $\Bbb Z\sb N$ Z N \Bbb Z\sb N . J. Anal. Math. 115 (2011), 121–186. MR2855033 Bourgain, J. ; Glibichuk, A. Exponential sum estimates over a subgroup in an arbitrary finite field. J. Anal. Math. 115 (2011), 51–70. MR2855016 Gusić, Ivica A remark on the Diophantine equation $f(x)=g(y)$ f ( x ) = g ( y ) f(x)=g(y) . Glas. Mat. Ser. III 46(66) (2011), no. 2, 333–338. MR2855015 Togbé, Alain ; Yuan, Pingzhi On a variant of a Diophantine equation of Cassels. Glas. Mat. Ser. III 46(66) (2011), no. 2, 325–331. MR2855014 Filipin, Alan ; Fujita, Yasutsugu The $D(-k\sp 2)$ D ( − k 2 ) D(-k\sp 2) -triple $\{1,k\sp 2+1,k\sp 2+4\}$ { 1 , k 2 + 1 , k 2 + 4 } \{1,k\sp 2+1,k\sp 2+4\} with $k$ k k prime. Glas. Mat. Ser. III 46(66) (2011), no. 2, 311–323. MR2855013 Jurasić, Ana Diophantine $m$ m m -tuples for quadratic polynomials. Glas. Mat. Ser. III 46(66) (2011), no. 2, 283–309. MR2855012 Matthews, Keith R. ; Robertson, John P. Period-length equality for the nearest integer and nearest square continued fraction expansions of a quadratic surd. Glas. Mat. Ser. III 46(66) (2011), no. 2, 269–282. MR2855004 Luca, Florian Erratum to the paper "Fibonacci numbers with the Lehmer property'' (Bull. Polish. Acad. Sci. Math. 55 (2007) 7--15) . Bull. Pol. Acad. Sci. Math. 59 (2011), no. 3, 289–290. MR2854998 Browkin, Jerzy ; Brzeziński, Juliusz ; Xu, Kejian On exceptions in the Brauer-Kuroda relations. Bull. Pol. Acad. Sci. Math. 59 (2011), no. 3, 207–214. MR2854996 Bibak, Khodakhast ; Shparlinski, Igor E. On fully split lacunary polynomials in finite fields. Bull. Pol. Acad. Sci. Math. 59 (2011), no. 3, 197–202. MR2854927 Kim, T. ; Dolgy, D. V. ; Lee, S. H. ; Lee, B. ; Rim, S. H. A note on the modified $q$ q q -Bernoulli numbers and polynomials with weight $\alpha$ α \alpha . Abstr. Appl. Anal. 2011, Art. ID 545314, 8 pp. MR2854833 Potgieter, Paul Arithmetic progressions in Salem-type subsets of the integers. J. Fourier Anal. Appl. 17 (2011), no. 6, 1138–1151. MR2854751 Spearman, Blair K. Arithmetic progressions on congruent number elliptic curves. Rocky Mountain J. Math. 41 (2011), no. 6, 2033–2044. MR2854739 Filipin, Alan There are only finitely many $D(4)$ D ( 4 ) D(4) -quintuples. Rocky Mountain J. Math. 41 (2011), no. 6, 1847–1859. MR2854738 Coffey, Mark W. On representations and differences of Stieltjes coefficients, and other relations. Rocky Mountain J. Math. 41 (2011), no. 6, 1815–1846. MR2893610 Hu, Weiqun Elliptic curves with an endomorphism of degree 3. Nanjing Daxue Xuebao Shuxue Bannian Kan 28 (2011), no. 1, 32–41. MR2854684 Zúiga-Galindo, W. A. Local zeta functions and fundamental solutions for pseudo-differential operators over $p$ p p -adic fields. p-Adic Numbers Ultrametric Anal. Appl. 3 (2011), no. 4, 344–358. MR2854682 Khrennikov, Andrei Yu. ; Van der Walt, Jan Harm On topological extensions of Archimedean and non-Archimedean rings. p-Adic Numbers Ultrametric Anal. Appl. 3 (2011), no. 4, 326–333. MR2854564 Gun, Sanoli ; Murty, M. Ram ; Rath, Purusottam Transcendental values of certain Eichler integrals. Bull. Lond. Math. Soc. 43 (2011), no. 5, 939–952. MR2854563 Jenkins, Paul ; Rouse, Jeremy Bounds for coefficients of cusp forms and extremal lattices. Bull. Lond. Math. Soc. 43 (2011), no. 5, 927–938. MR2854224 Guo, Victor J. W. ; Zeng, Jiang Factors of sums and alternating sums involving binomial coefficients and powers of integers. Int. J. Number Theory 7 (2011), no. 7, 1959–1976. MR2854223 Huber, Tim Differential equations for cubic theta functions. Int. J. Number Theory 7 (2011), no. 7, 1945–1957. MR2854222 Li, Yan ; Ma, Lianrong Double coverings and unit square problems for cyclotomic fields. Int. J. Number Theory 7 (2011), no. 7, 1935–1944. MR2854221 Bouganis, Thanasis Non-abelian congruences between special values of $L$ L L -functions of elliptic curves: the CM case. Int. J. Number Theory 7 (2011), no. 7, 1883–1934. MR2854220 Reznick, Bruce ; Rouse, Jeremy On the sums of two cubes. Int. J. Number Theory 7 (2011), no. 7, 1863–1882. MR2854219 Petersen, Kathleen L. ; Sinclair, Christopher D. Equidistribution of algebraic numbers of norm one in quadratic number fields. Int. J. Number Theory 7 (2011), no. 7, 1841–1861. MR2854218 Zumalacárregui, Ana Concentration of points on modular quadratic forms. Int. J. Number Theory 7 (2011), no. 7, 1835–1839. MR2854217 Berger, Laurent A $p$ p p -adic family of dihedral $(\phi,\Gamma)$ ( φ , Γ ) (\phi,\Gamma) -modules. Int. J. Number Theory 7 (2011), no. 7, 1825–1834. MR2854214 Ribenboim, Paulo Multiple patterns of $k$ k k -tuples of integers. Int. J. Number Theory 7 (2011), no. 7, 1761–1779. MR2854213 Bazzanella, Danilo Two conditional results about primes in short intervals. Int. J. Number Theory 7 (2011), no. 7, 1753–1759. MR2854212 Hare, Kevin G. ; Laishram, Shanta ; Stoll, Thomas The sum of digits of $n$ n n and $n\sp 2$ n 2 n\sp 2 . Int. J. Number Theory 7 (2011), no. 7, 1737–1752. MR2854211 Ballot, Christian ; Car, Mireille On Murata densities. Int. J. Number Theory 7 (2011), no. 7, 1717–1736. MR2854210 Knopfmacher, Arnold ; Luca, Florian On prime-perfect numbers. Int. J. Number Theory 7 (2011), no. 7, 1705–1716. MR2853348 Kim, T. ; Lee, S. H. ; Han, Hyeon-Ho ; Ryoo, C. S. On the values of the weighted $q$ q q -zeta and $L$ L L -functions. Discrete Dyn. Nat. Soc. 2011, Art. ID 476381, 7 pp. MR2893564 Vagabov, A. I. Asymptotic representations of series and some problems in number theory. (Russian) Dokl. Akad. Nauk 439 (2011), no. 4, 439--442; translation in Dokl. Math. 84 (2011), no. 1, 506–509 MR2854120 Rohrlich, David E. Galois invariance of local root numbers. Math. Ann. 351 (2011), no. 4, 979–1003. MR2854115 Murty, M. Ram ; Murty, V. Kumar Transcendental values of class group $L$ L L -functions. Math. Ann. 351 (2011), no. 4, 835–855. MR2852010 Alperin, Roger C. Integer sequences generated by $x\sb {n+1}=\frac{x\sp 2\sb n+A}{x\sb {n-1}}$ x n + 1 = x 2 n + A x n − 1 x\sb {n+1}=\frac{x\sp 2\sb n+A}{x\sb {n-1}} . Fibonacci Quart. 49 (2011), no. 4, 362–365. MR2852009 Griffiths, Martin Binet-like formulas from a simple expansion. Fibonacci Quart. 49 (2011), no. 4, 355–361. MR2852008 Sills, Andrew V. Compositions, partitions, and Fibonacci numbers. Fibonacci Quart. 49 (2011), no. 4, 348–354. MR2852006 Baczkowski, Daniel ; Fasoranti, Olaolu ; Finch, Carrie E. Lucas-Sierpiński and Lucas-Riesel numbers. Fibonacci Quart. 49 (2011), no. 4, 334–339. MR2852005 Steuding, Jrn What Fibonacci numbers have to do with congruent numbers? Fibonacci Quart. 49 (2011), no. 4, 330–333. MR2852004 Kili, Emrah ; Prodinger, Helmut ; Akkus, Ilker ; Ohtsuka, Hideyuki Formulas for Fibonomial sums with generalized Fibonacci and Lucas coefficients. Fibonacci Quart. 49 (2011), no. 4, 320–329. MR2852003 Klaška, Jiří ; Skula, Ladislav Mordell's equation and the Tribonacci family. Fibonacci Quart. 49 (2011), no. 4, 310–319. MR2852002 Anderson, Peter G. ; Cooper, Curtis Every positive $k$ k k -bonacci-like sequence eventually agrees with a row of the $k$ k k -Zeckendorf array. Fibonacci Quart. 49 (2011), no. 4, 303–309. MR2852001 Šiurys, Jonas A tribonacci-like sequence of composite numbers. Fibonacci Quart. 49 (2011), no. 4, 298–302. MR2868028 Zhang, Zhen Liang Engel continued fraction expansion and Hausdorff dimension. (Chinese) Math. Appl. (Wuhan) 24 (2011), no. 3, 641–644. MR2853788 Cooper, Shaun ; Hirschhorn, Michael D. Factorizations that involve Ramanujan's function $k(q)=r(q)r\sp 2(q\sp 2)$ k ( q ) = r ( q ) r 2 ( q 2 ) k(q)=r(q)r\sp 2(q\sp 2) . Acta Math. Sin. (Engl. Ser.) 27 (2011), no. 12, 2301–2308. MR2853716 Dasdemir, Ahmet On the Pell, Pell-Lucas and modified Pell numbers by matrix method. Appl. Math. Sci. (Ruse) 5 (2011), no. 61-64, 3173–3181. MR2893524 Skriganov, M. M. The Khinchin inequality and Chen's theorem. (Russian) Algebra i Analiz 23 (2011), no. 4, 179–204. MR2893520 Golovchanskiĭ, V. V. ; Smotrov, M. N. On the spectrum of the Laplace-Beltrami operator for some congruence subgroups of the modular group. (Russian) Algebra i Analiz 23 (2011), no. 4, 31–39. MR2885100 Jung, Hwanyup ; Yue, Qin 8-ranks of class groups of imaginary quadratic number fields and their densities. J. Korean Math. Soc. 48 (2011), no. 6, 1249–1268. MR2885086 Dombek, D. ; Masáková, Z. ; Pelantová, E. Number representation using generalized $(-\beta)$ ( − β ) (-\beta) -transformation. Theoret. Comput. Sci. 412 (2011), no. 48, 6653–6665. MR2884906 Batir, Necdet Sharp bounds for the psi function and harmonic numbers. Math. Inequal. Appl. 14 (2011), no. 4, 917–925. MR2853229 Shparlinski, Igor E. Character sums with Fermat quotients. Q. J. Math. 62 (2011), no. 4, 1031–1043. MR2853093 Shen, Luming ; Fang, Kui The fractional dimensional theory in Lüroth expansion. Czechoslovak Math. J. 61(136) (2011), no. 3, 795–807. MR2853089 Guo, Xiaoyan ; Zhang, Wenpeng A hybrid mean value related to certain Hardy sums and Kloosterman sums. Czechoslovak Math. J. 61(136) (2011), no. 3, 759–769. MR2777812 Arias-de-Reyna, Sara ; Vila, Núria Galois representations and the tame inverse Galois problem. WIN—women in numbers, 277–288, Fields Inst. Commun., 60, Amer. Math. Soc., Providence, RI, 2011. MR2777811 Ramdorai, Sujatha On the $\mu$ μ \mu -invariant in Iwasawa theory. WIN—women in numbers, 265–276, Fields Inst. Commun., 60, Amer. Math. Soc., Providence, RI, 2011. MR2777803 Berger, Lisa ; Hoelscher, Jing Long ; Lee, Yoonjin ; Paulhus, Jennifer ; Scheidler, Renate The $\ell$ ℓ \ell -rank structure of a global function field. WIN—women in numbers, 145–166, Fields Inst. Commun., 60, Amer. Math. Soc., Providence, RI, 2011. MR2777802 Bucur, Alina ; David, Chantal ; Feigon, Brooke ; Lalín, Matilde Biased statistics for traces of cyclic $p$ p p -fold covers over finite fields. WIN—women in numbers, 121–143, Fields Inst. Commun., 60, Amer. Math. Soc., Providence, RI, 2011. MR2777800 Mantovan, Elena $l$ l l -adic étale cohomology of PEL type Shimura varieties with non-trivial coefficients. WIN—women in numbers, 61–83, Fields Inst. Commun., 60, Amer. Math. Soc., Providence, RI, 2011. MR2777799 Grundman, Helen ; Johnson-Leung, Jennifer ; Lauter, Kristin ; Salerno, Adriana ; Viray, Bianca ; Wittenborn, Erika Igusa class polynomials, embeddings of quartic CM fields, and arithmetic intersection theory. WIN—women in numbers, 35–60, Fields Inst. Commun., 60, Amer. Math. Soc., Providence, RI, 2011. MR2777797 Grundman, Helen Hilbert modular variety computations. WIN—women in numbers, 3–14, Fields Inst. Commun., 60, Amer. Math. Soc., Providence, RI, 2011. MR2777796 WIN—women in numbers. 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MR2856561 Giulietti, M. ; Hirschfeld, J. W. P. ; Korchmáros, G. ; Torres, F. A family of curves covered by the Hermitian curve. Arithmetics, geometry, and coding theory (AGCT 2005), 63–78, Sémin. Congr., 21, Soc. Math. France, Paris, 2010. MR2856557 Betsumiya, Koichi ; Choie, YoungJu Invariant ring of Clifford-Weil group, and Jacobi forms over totally real field. Arithmetics, geometry, and coding theory (AGCT 2005), 1–16, Sémin. Congr., 21, Soc. Math. France, Paris, 2010. MR2894710 Simonov, A. S. On the error of approximate integration over modified grids. (Russian) Chebyshevskiĭ Sb. 9 (2008), no. 1(25), 185–223. ISBN: 978-5-87954-483-1 MR2894709 Budarina, Natalia ; Dickinson, Detta Simultaneous Diophantine approximation of integral polynomials in the different metrics. Chebyshevskiĭ Sb. 9 (2008), no. 1(25), 169–184. ISBN: 978-5-87954-483-1 MR2894384 Kopaneva, A. A. An estimate for short sums of Dirichlet characters over shifted primes. (Russian) Chebyshevskiĭ Sb. 9 (2008), no. 1(25), 122–143. ISBN: 978-5-87954-483-1 MR2894382 Gorkusha, O. A. On finite continued fractions of a special type. (Russian) Chebyshevskiĭ Sb. 9 (2008), no. 1(25), 79–107. ISBN: 978-5-87954-483-1 MR2894381 Burlakova, E. A. The Waring-Goldbach problem. (Russian) Chebyshevskiĭ Sb. 9 (2008), no. 1(25), 69–79. ISBN: 978-5-87954-483-1 MR2894375 Allakov, I. On Goldbach numbers. (Russian) Chebyshevskiĭ Sb. 9 (2008), no. 1(25), 4–8. ISBN: 978-5-87954-483-1
“第7届国际数论与Smarandache问题研讨会（7th international coference on number thoery and Smarandache problems）”2011年3月25-27日在渭南师范学院召开，来自日本、俄罗斯、西班牙、印度以及中国大陆地区的20多所高等院校以及研究机构的120余人参加，他们分别来自中国科学院、西北大学、西安交通大学、浙江师范大学、海南师范大学、西南大学、空军工程大学、西北工业大学、西安工程大学、西安建筑科技大学、长安大学、咸阳师范学院、西藏民族学院、陕西师范大学、延安大学、西北政法大学、西安财经学院、南阳师范学院、惠州学院、西安邮电学院、天水师范学院、西安文理学院、宝鸡文理学院、西安财经学院、榆林学院、安康学院、西安航空职业技术学院、宝鸡职业技术学院等院校，也有来自湖北宜昌、广东深圳的数论爱好者以及部分数论方向的在读的硕士、博士研究生。大会交流作者21名，其中有印度、日本、俄罗斯、西班牙各一名，其余17名均来自中国大陆。大会执行主席分别由西北大学的张文鹏教授，西安交通大学的李媛教授，印度Harish Chandra研究所的Kalyan Chakraborty教授(Asst. Professor at Harish Chandra Research Institute)、西班牙加泰罗尼 亚理工大学( Universitat Politècnica de Catalunya )应用数学系（ Department of Applied Mathematics IV ）Jorge Jiménez Urroz副教授（Associate professor）以及日本近畿大学(Kinki University)金光滋（ Shigeru Kanemitsu ）教授担任。 本次会议的国际预报 March 25– March 27, 2011 The Seventh International Conference on Number Theory and Smarandache Notions Weinan Teachers University, Weinan, Shaanxi, People's Republic of China http://aimsciences.org/Meetings/index.htm ， 2010年第6届国际数论与Smarandache问题研讨会论文集 http://fs.gallup.unm.edu/ChinaSmConf6.pdf 通过参加本次会议以及与学报界同仁的交流座谈，使我深深感到渭南师范学院对于数学研究、对于学报编辑出版工作、对于科学研究工作的支撑力度之大，可以说是前所未有的。新面貌出现反映出学院领导的新思路，大谋略。可敬可赞，难得如此！
仰望星空的空竹丫头妹子，确实魅力无穷。我也追着大伙，再一次仰望我们头顶上的星空。不过这里我要告诉你们大伙，星空在它总是表现为如此美丽的同时，她还时不时地表现得非常地无理。 容我先在科学网上的众多数学界与天文学界的鲁班们面前，舞弄一下我手中的好大一把斧头，圈一圈我用来玩杂耍的场子。 我们都知道，数有无理数与有理数，什么是无理数？请别问我，直接去问上帝他老哥去，由他负责给我们大家科普。但我可以告诉大伙，自然界中，有一些我们所知道的无理数，很有名气，例如 e=2.718 ，还有 PI=3.14159 ，对了。我这里先谈 PI ， PI 这个无理的家伙，如何搅乎得我们头顶上原本美丽的星空，同时也变得如此无理。 实际上，我们人类对于星空表现为如此无理的这种认识，甚至可以追溯到远古时代的巴比伦、埃及和中国。其中，阿基米德所建立的 PI 值理论估算，在数学发展史上具有重要的历史地位。 PI 值同时也与几何学中著名的布丰（ Buffon） 落针实验的概率问题紧密联系；但如说咱们中国人的话，那么祖乃 甡 先生的祖上祖冲之对PI的贡献是肯定绕不开的。 2001 年8月6日， Nature的NSU栏目， 曾以 PI 相关热点问题， 报道了是时数学界关于 PI 值的研究方面所引发的一些混乱。 更具体一些，又是哪位科学家舞动 PI 的大棒，使得原本美丽的星空，变得如此无理呢？ 答案是，一个名叫马休斯（ Matthews） 的老兄，与《悲惨世界》的那个男主人公之一的名字，取得一模一样。 首先，马休斯 在 我们头顶上的星空中，根据星星的星等亮度，选取了 100 颗最为明亮的星星，计算这些明亮星星间的角距离。然后，马休斯拿来了一把尺子，当然，这把尺子的刻度大小要比较恰当，不能够刻度间隔太长，好比你拿一把每隔 1 公里 长一个刻度的尺子，去度量一个人的身高一般；当然也不能够太短，太短了你量出来一个人的身高，就变成了这个人身高多少多少乘以 10 的多少多少次方纳米了。 回过头来，马休斯知道了这些角距离，也拿到了一把非常顺手的尺子以后，他便开始用这把尺子，一个一个地度量这些角距离，并且记下它们的读数。简单说吧，如果读出来某个角距离为 8926.85 尺子单位，马休斯很大方，把小数点后面的 0.85 扔掉，他只记下 8926 这个整数来。 马休斯人很努力啊， 不怕麻烦，就用这把尺子，采用上面的办法，在天空当中最为明亮的这 100 个星星中，任意抽取两个星星，度量其角距离，用尺子度量，然后得到了相应的整数。大伙可以算算，这些所有整数的数量应该很多很多吧，具体有多少？我估计，应该与电视上见到的福利彩票机的吐小球游戏差不多，也就是说，与在 100 个不同颜色的小球中，随机抽取两个小球出来，问有多少种不同抽取办法的这种情况相类似。 剩下的事情就变得非常简单，马休斯利用分析数论 的相关知识：任意随机选取两个 整数 , 它们 相对互素（即除 1 以外没有其它公约数 ) 的概率为 6/PI 2 。这样，马休斯通过他已经得到的所有这些整数，任取两个整数，看看他们是否互为素数。 一番劳累之后，马休斯得出结论，以此分析数论的 PI 值估算方式，得到了估计出来的 PI 值关于真值的相对误差，竟然小于 0.4% 的有意思的结论。也就是说，对位于我们头顶上最为明亮的 100 颗星星，通过马休斯所进行的一番捣鼓，他给出了 PI 介于 3.1414 与 3.1417 之间的数值估计。 大伙看看，马休斯 这位老兄是不是很 牛？还有，我们头顶上的美丽星空，表现得是不是也很无理？ 参考文献 Matthews R A J. ， Pi in the sky ， . Nature, 1995, 374: 681~682. Jones G A, Jones J M. Elementary Number Theory . London : Springer-Verlag, 1998.
标签: 数论
