MR2016年9月份数论最新文献题录300条（见附件）

诸平 辑

关于美国《数学评论》（MR）数据库题录数论研究最新信息，从2012年4月以来已经连续搜索与转载报道有几年时间了，2013年1-12月的逐月统计结果已有报道，见MR2013年12月份数论最新文献题录241条。MR2014年1～12月份数论题录文献检索结果,详见：

MR2014年12月份数论研究最新文献题录197条，

MR2015年1～12月份数论题录文献检索结果,详见：

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MR2016年9月份收录文献总量为9735条，其中数论研究最新文献题录300条，摘录部分如下（可能存在数学公式无法准确显示或者出现乱码，请读者参考原文献），更多可以参考附件.

MR2016-09-300 for Number Theory.pdf

MR3522253 Deppe, Holger p-adic L-functions of automorphicforms and exceptional zeros. Doc. Math.21 (2016), 689–734.

MR3522250 Burns, David; Kurihara, Masato; Sano, Takamichi On zeta elements for $\Bbb G\sb m$. Doc.Math. 21 (2016), 555–626.

MR3522086 Ahmed, Zakir; Baruah, Nayandeep Deka New congruencesfor $\ell$-regular partitions for$\ell\in\{5,6,7,49\}$. RamanujanJ. 40 (2016), no. 3,649–668.

MR3522085 Bachmann, Henrik; Kühn, Ulf The algebra of generating functions formultiple divisor sums and applications to multiple zeta values. RamanujanJ. 40 (2016), no. 3,605–648.

MR3522083 Hu, Liqun; Liu, Huafeng Sum of divisors of a quaternaryquadratic form with almost equal variables. Ramanujan J. 40 (2016), no. 3, 557–571.

MR3522081 Dou, Donna Q. J. Congruences for $(3,11)$-regularbipartitions modulo 11. Ramanujan J. 40 (2016), no. 3, 535–540.

MR3522080 Sun, Zhi-Wei Congruences involving $g\sbn(x)=\sum\sp n\sb {k=0}\binom nk\sp 2\binom{2k}kx\sp k$. Ramanujan J. 40 (2016), no. 3, 511–533.

MR3522078 Zhou, Roberta R. Some new identities for coloredpartition. Ramanujan J. 40 (2016), no. 3, 473–490.

MR3522077 Hirschhorn, Michael D. Somecongruences for 6-colored generalized Frobenius partitions.Ramanujan J. 40 (2016), no. 3, 463–471.

MR3518161 Stoll, Thomas On digital blocks of polynomial valuesand extractions in the Rudin-Shapiro sequence. RAIRO Theor. Inform.Appl. 50 (2016), no. 1,93–99.

MR3518159 Brunotte, Horst Digital semigroups. RAIROTheor. Inform. Appl. 50(2016), no. 1, 67–79.

MR3512883 Languasco, Alessandro; Perelli, Alberto; Zaccagnini, Alessandro An extension ofthe pair-correlation conjecture and applications. Math. Res. Lett. 23 (2016), no. 1, 201–220.

MR3512882 Lan, Kai-Wen Higher Koecher's principle. Math.Res. Lett. 23 (2016),no. 1, 163–199.

MR3512875 Billerey, Nicolas; Menares, Ricardo On the modularity of reducible ${\rmmod}\, l$ Galois representations. Math. Res. Lett. 23 (2016), no. 1, 15–41.

MR3497855 Tubbs, Robert Hilbert's seventh problem. Solutions and extensions. Institute ofMathematical Sciences Lecture Notes, 2. HindustanBook Agency, New Delhi, 2016.85 pp. ISBN: 978-93-80250-82-3

MR3521911 Samart, Detchat Feynman integrals and critical modular $L$-values. Commun.Number Theory Phys. 10(2016), no. 1, 133–156.

MR3521908 Harvey, Jeffrey A.; Rayhaun, Brandon C. Traces of singular moduli and moonshinefor the Thompson group. Commun. Number Theory Phys. 10 (2016), no. 1, 23–62.

MR3521907 Luu, Martin T. Local Langlands duality and a dualityof conformal field theories. Commun. Number Theory Phys. 10 (2016), no. 1, 1–22.

MR3521539 Nguyen, Phong Q.; Shparlinski, Igor E. Counting co-cyclic lattices. SIAMJ. Discrete Math. 30(2016), no. 3, 1358–1370.

MR3517081 Ahn, Jaehyun On the ratio of relative congruencezeta functions of cyclotomic function fields.J. Chungcheong Math. Soc. 29 (2016), no. 1, 117–121.

MR3510986 Williams, Kenneth S. Bounds for the representations ofintegers by positive quadratic forms.Math. Mag. 89 (2016), no. 2, 122–131.

MR3509724 Truman, Paul J. Hopf-Galois module structure of tame Cp×Cp extensions. J.Théor. Nombres Bordeaux 28(2016), no. 2, 557–582.

MR3509722 Lü, Xiaodong; Mu, Quanwu On Waring-Goldbach problem of mixedpowers. J. Théor. Nombres Bordeaux 28 (2016), no. 2, 523–538.

MR3509721 Izychev, Dmitriy; Venjakob, Otmar Equivariant epsilon conjecture for1-dimensional Lubin-Tate groups. J. Théor. Nombres Bordeaux 28 (2016), no. 2, 485–521.

MR3509720 Adiceam, Faustin Liminf sets in simultaneous Diophantineapproximation. J. Théor. Nombres Bordeaux 28 (2016), no. 2, 461–483.

MR3509719 Roberts, David P. Lightly ramified number fields withGalois group S.M12.A. J. Théor.Nombres Bordeaux 28(2016), no. 2, 435–460.

MR3509718 Nicolae, Florin On the determination of number fieldsby L-functions. J. Théor. Nombres Bordeaux 28 (2016), no. 2, 431–433.

MR3509717 Cais, Bryden; Davis, Christopher; Lubin, Jonathan A characterization of strictly APFextensions. J. Théor. Nombres Bordeaux 28 (2016), no. 2, 417–430.

MR3509714 Bengoechea, Paloma Galois action on special theta values. J.Théor. Nombres Bordeaux 28(2016), no. 2, 347–360.

MR3509713 Ichimura, Humio; Sumida-Takahashi, Hiroki Normal integralbasis of an unramified quadratic extension over a cyclotomic Z2-extension. J.Théor. Nombres Bordeaux 28(2016), no. 2, 325–345.

MR3509711 Bhowmik, Gautami; Ramaré, Olivier; Schlage-Puchta, Jan-Christoph Tauberianoscillation theorems and the distribution of Goldbach numbers. J.Théor. Nombres Bordeaux 28(2016), no. 2, 291–299.

MR3521360 Khan, Rizwanur The divisor function in arithmeticprogressions modulo prime powers.Mathematika 62 (2016), no. 3, 898–908.

MR3521359 Coons, Michael; Hussain, Mumtaz; Wang, Bao-Wei A dichotomy law for the diophantineproperties in β-dynamical systems. Mathematika 62 (2016), no. 3, 884–897.

MR3521358 Lau, Yuk-kam; Royer, Emmanuel; Wu, Jie Sign of Fourier coefficients of modularforms of half-integral weight. Mathematika 62 (2016), no. 3, 866–883.

MR3521357 Chan, Tsz Ho Shortest distance in modular hyperbolaand least quadratic non-residue.Mathematika 62 (2016), no. 3, 860–865.

MR3521356 Shparlinski, Igor E. On bilinear exponential and charactersums with reciprocals of polynomials. Mathematika 62 (2016), no. 3, 842–859.

MR3521353 Krishnamoorthy, Srilakshmi; Murty, M. Ram On sign changes for almost primecoefficients of half-integral weight modular forms. Mathematika 62 (2016), no. 3, 801–810.

MR3521352 Li, Liangpan The Duffin–Schaeffer-type conjecturesin various local fields. Mathematika 62 (2016), no. 3, 753–800.

MR3521343 Henriot, Kevin Arithmetic progressions in sets ofsmall doubling. Mathematika 62 (2016), no. 2, 587–613.

MR3521342 Harman, Glyn Primes in Beatty sequences in shortintervals. Mathematika 62 (2016), no. 2, 572–586.

MR3521341 Heath-Brown, D. R. Small solutions of quadraticcongruences, and character sums with binary quadratic forms. Mathematika 62 (2016), no. 2, 551–571.

MR3521340 Akbal, Yıldırım; Güloğlu, Ahmet M. Waring's problem with Piatetski-Shapironumbers.Mathematika 62(2016), no. 2, 524–550.

MR3521339 Huang, Bingrong Exponential sums over primes in shortintervals and an application to the Waring-Goldbach problem. Mathematika 62 (2016), no. 2, 508–523.

MR3521338 Dummit, David; Granville, Andrew; Kisilevsky, Hershy Big biases amongst products of twoprimes. Mathematika 62 (2016), no. 2, 502–507.

MR3521336 Aistleitner, Christoph; Larcher, Gerhard Metric results on the discrepancy ofsequences (anα)n⩾1 modulo one for integer sequences (an)n⩾1 of polynomial growth. Mathematika 62 (2016), no. 2, 478–491.

MR3521334 Xue, Boqing; Zhao, Lilu Rational points on cubic hypersurfacesthat split into four forms.Mathematika 62 (2016), no. 2, 430–440.

MR3521333 Kıral, Eren Mehmet Opposite-sign Kloosterman sum zetafunction. Mathematika 62 (2016), no. 2, 406–429.

MR3516180 Lu, Yaming Almost-primes represented by p+am. Korean J.Math. 24 (2016), no. 1,107–138.

MR3516178 Kim, Byeong Moon Representation of a positive integer bya sum of large four squares.Korean J. Math. 24 (2016), no. 1, 71–79.

MR3495862 Tang, Min Partitions of natural numbers and theirrepresentation functions. (Chinese)Chinese Ann. Math.Ser. A 37 (2016), no. 1,41–46.

MR3521155 Tan, Qianrong; Lin, Zongbing; Chen, Long Divisibility among power matricesassociated with arithmetic functions on finitely many quasi-coprime divisorchains. Linear Multilinear Algebra 64 (2016), no. 10, 2030–2048.

MR3521147 Wang, Bangyan; Hong, Shaofang; Li, Mao Hyperdeterminants on meet-semilattices. LinearMultilinear Algebra 64(2016), no. 10, 1899–1915.

MR3521092 Daw, Christopher; Orr, Martin Heights of pre-special points ofShimura varieties. Math. Ann.365 (2016), no. 3-4, 1305–1357.

MR3520586 Dixit, Atul; Glasser, M. Lawrence; Moll, Victor H.; Vignat, Christophe Asymptotics and exact formulas forZagier polynomials. Res. Number Theory 2 (2016), Art. 12, 26 pp.

MR3520435 Kraus, Alain Contre-exemples au principe de Hassepour les courbes de Fermat. (French)[Counterexamples to the Hasse principle for Fermat curves] Acta Arith. 174 (2016), no. 2, 189–197.

MR3520433 Balkanova, Olga The shifted fourth moment ofautomorphic L-functions of prime power level.ActaArith. 174 (2016),no. 2, 121–174.

MR3520432 Jędrzejak, Tomasz On the torsion of the Jacobians of thehyperelliptic curves y2=xn+a and y2=x(xn+a). Acta Arith. 174 (2016), no. 2, 99–120.

MR3520272 Plagne, Alain; Tringali, Salvatore Sums of dilates in ordered groups. Comm.Algebra 44 (2016),no. 12, 5223–5236.

MR3520259 Chen, William Y. C.; Hou, Qing-Hu; Zeilberger, Doron Automated discovery and proof ofcongruence theorems for partial sums of combinatorial sequences. J.Difference Equ. Appl. 22(2016), no. 6, 780–788.

MR3520238 Qi, Feng; Jang, Lee-Chae; Kwon, Hyuck-In Some new and explicit identitiesrelated with the Appell-type degenerate q-Changheepolynomials. Adv. Difference Equ. 2016, 2016:180, 8 pp.

MR3495993 Sładek, Andrzej Linear dependence of powers of linearforms. Ann. Math. Sil. No. 29 (2015), 131–138.

MR3496675 Capuano, Laura; Del Corso, Ilaria A note on upper ramification jumps inAbelian extensions of exponent p. Riv. Math. Univ. Parma (N.S.) 6 (2015), no. 2, 317–329.

MR3444237 Khare, Chandrashekhar; Wintenberger, Jean-Pierre Intertwining oframified and unramified zeros of Iwasawa modules. Automorphic forms andGalois representations. Vol. 2, 367–378, London Math. Soc. Lecture Note Ser., 415, CambridgeUniv. Press, Cambridge, 2014.

MR3444236 Schneider, Peter; Vigneras, Marie-France; Zabradi, Gergely From étale P+-representations toG-equivariant sheaveson G/P. Automorphicforms and Galois representations. Vol. 2, 248–366, London Math. Soc. Lecture Note Ser., 415, CambridgeUniv. Press, Cambridge, 2014.

MR3444233 Haines, Thomas J. The stable Bernstein center and testfunctions for Shimura varieties.Automorphic forms and Galoisrepresentations. Vol. 2, 118–186, London Math. Soc. Lecture Note Ser., 415,Cambridge Univ.Press, Cambridge, 2014.

MR3444232 Furusho, Hidekazu Around associators. Automorphicforms and Galois representations. Vol. 2,105–117, London Math. Soc. Lecture Note Ser., 415, CambridgeUniv. Press, Cambridge, 2014.

MR3444231 Fargues, Laurent; Fontaine, Jean-Marc Vector bundles on curves and p-adic Hodge theory.Automorphicforms and Galois representations. Vol. 2, 17–104, London Math. Soc. Lecture Note Ser., 415,Cambridge Univ.Press, Cambridge, 2014.

MR3444230 Dimitrov, Mladen On the local structure of ordinaryHecke algebras at classical weight one points. Automorphic forms andGalois representations. Vol. 2, 1–16, London Math. Soc. Lecture Note Ser., 415, CambridgeUniv. Press, Cambridge, 2014.

MR3444229 Dospinescu, Gabriel Equations différentielles p-adiques et modulesde Jacquet analytiques.(French)[p-adic differentialequations and analytic Jacquet modules] Automorphicforms and Galois representations. Vol. 1, 359–374, London Math. Soc. Lecture Note Ser., 414, CambridgeUniv. Press, Cambridge, 2014.

MR3444228 Colmez, Pierre La série principale unitaire de GL2(Qp): vecteurs localementanalytiques.(French) [The unitaryprincipal series of GL2(Qp): locally analyticvectors] Automorphicforms and Galois representations. Vol. 1, 286–358, London Math. Soc. Lecture Note Ser., 414, CambridgeUniv. Press, Cambridge, 2014.

MR3444227 Chenevier, Gaëtan The p-adic analytic spaceof pseudocharacters of a profinite group and pseudorepresentations overarbitrary rings. Automorphic forms and Galois representations. Vol. 1, 221–285, London Math. Soc. Lecture NoteSer., 414, Cambridge Univ. Press, Cambridge, 2014.

MR3444226 Chaudouard, Pierre-Henri Geometry of thefundamental lemma. Automorphic forms and Galois representations. Vol.1, 188–220, London Math.Soc. Lecture Note Ser., 414, Cambridge Univ. Press, Cambridge, 2014.

MR3444225 Buzzard, Kevin; Gee, Toby The conjectural connections betweenautomorphic representations and Galois representations. Automorphicforms and Galois representations. Vol. 1, 135–187, London Math. Soc. Lecture Note Ser., 414, CambridgeUniv. Press, Cambridge, 2014.

MR3444223 Bertolini, Massimo; Castella, Francesc; Darmon, Henri; Dasgupta, Samit; Prasanna, Kartik;Rotger, Victor p-adic L-functions and Eulersystems: a tale in two trilogies. Automorphic forms and Galoisrepresentations. Vol. 1, 52–101, London Math. Soc. Lecture Note Ser., 414, CambridgeUniv. Press, Cambridge, 2014.

MR3444222 Berger, Laurent; Vienney, Mathieu Irreducible modular representations ofthe Borel subgroup of GL2(Qp). Automorphic forms and Galoisrepresentations. Vol. 1, 32–51, London Math. Soc. Lecture Note Ser., 414, CambridgeUniv. Press, Cambridge, 2014.

MR3444221 Abrashkin, Victor A semi-stable case of the Shafarevichconjecture. Automorphic forms and Galois representations. Vol. 1, 1–31, London Math. Soc. Lecture Note Ser.,414, CambridgeUniv. Press, Cambridge, 2014.

MR3410215 Automorphicforms and Galois representations. Vol. 2. Proceedings of the 94th London Mathematical SocietyLMS-EPSRC Symposium on Galois Representations and Automorphic Forms held at theUniversity of Durham, Durham, July 18–28, 2011. Edited by Fred Diamond, PaymanL. Kassaei and Minhyong Kim. London Mathematical Society Lecture Note Series,415. CambridgeUniversity Press, Cambridge, 2014. vii+378 pp. ISBN: 978-1-107-69363-0

MR3410214 Automorphicforms and Galois representations. Vol. 1. Proceedings of the 94th London Mathematical SocietyLMS-EPSRC Symposium on Galois Representations and Automorphic Forms held at theUniversity of Durham, Durham, July 18–28, 2011. Edited by Fred Diamond, PaymanL. Kassaei and Minhyong Kim. London Mathematical Society Lecture Note Series,414. CambridgeUniversity Press, Cambridge, 2014. ix+374 pp. ISBN: 978-1-107-69192-6

MR3515664 Aguiló-Gost, F.; García-Sánchez, P. A.; Llena, D. An algorithm to compute the primitiveelements of an embedding dimension three numerical semigroup. Conferenceon Discrete Mathematics and Computer Science (Spanish), 185–192, Electron. Notes Discrete Math.,46, ElsevierSci. B. V., Amsterdam,2014.

MR3515641 Aguiló-Gost, F.; García-Sánchez, P. A.; Llena, D. Denumerants of 3-numerical semigroups.Conferenceon Discrete Mathematics and Computer Science (Spanish), 3–10, Electron. Notes Discrete Math., 46, ElsevierSci. B. V., Amsterdam, 2014.