MR2016年12月份数论最新文献题录218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：

MR2015年1~12月份数论最新文献题录

MR2016年1月份数论最新文献题录186条

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MR2016年12月份收录文献总量为8632条，其中数论研究最新文献题录218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.

MR2016-12-218 for Number Theory.pdf

MR3557779 Schmidt, Kai-Uwe Thecorrelation measures of finite sequences: limiting distributions and minimum values. Trans.Amer. Math. Soc. 369 (2017), no. 1, 429–446.

MR3561734 Dorward, Robert; Ford, Pari L.; Fourakis, Eva; Harris, PamelaE.; Miller, StevenJ.; Palsson,Eyvindur; Paugh, Hannah Ageneralization of Zeckendorf's theorem via circumscribed $m$-gons. Involve 10(2017), no. 1, 125–150.

MR3558223 Berndt, Bruce C.; Dixit, Atul; Roy, Arindam; Zaharescu,Alexandru New pathways and connections in number theory andanalysis motivated by two incorrect claims of Ramanujan. Adv. Math. 304(2017), 809–929.

MR3558213 Cowan, RaemeonA.; Katz, Daniel J.; White, Lauren M. Anew generating function for calculating the Igusa local zeta function. Adv.Math. 304 (2017), 355–420.

MR3556695 Göral, Haydar; Sertbaş, DoğaCan Almost all hyperharmonic numbers are not integers. J.Number Theory 171 (2017), 495–526.

MR3556694 Taleb, Reza Anequivariant main conjecture in Iwasawa theory without the assumption $\mu=0$.J.Number Theory 171 (2017), 474–494.

MR3556693 Vatwani, Akshaa Boundedgaps between Gaussian primes. J. Number Theory 171 (2017),449–473.

MR3556692 Pethő, Attila; Pohst, MichaelE.; Bertók, Csanád Onmultidimensional Diophantine approximation of algebraic numbers. J.Number Theory 171 (2017), 422–448.

MR3556691 de Shalit, Ehud; Goren, Eyal Z. Supersingularcurves on Picard modular surfaces modulo an inert prime. J. NumberTheory 171 (2017), 391–421.

MR3556690 Loquias, ManuelJoseph C.; Mkaouar, Mohamed; Scheicher, Klaus; Thuswaldner,Jörg M. Rational digit systems over finite fields and Christol'stheorem. J. Number Theory 171 (2017), 358–390.

MR3556689 Anbar, Nurdagül; Bassa, Alp; Beelen, Peter Amodular interpretation of various cubic towers. J. Number Theory 171(2017), 341–357.

MR3556688 Choi, Dohoon; Lim, Subong; Mühlenbruch,Tobias; Raji, Wissam Seriesexpansion of the period function and representations of Hecke operators. J.Number Theory 171 (2017), 301–340.

MR3556687 Hürlimann,Werner On universal zero-free ternary quadratic formrepresentations of primes in arithmetic progressions. J. Number Theory 171(2017), 284–300.

MR3556686 Sun, Zhi-Wei On $x(ax+1)+y(by+1)+z(cz+1)$ and $x(ax+b)+y(ay+c)+z(az+d)$. J.Number Theory 171 (2017), 275–283.

MR3556685 Sun, Chaochao; Xu, Kejian Ontame kernels and second regulators of number fields and their subfields. J.Number Theory 171 (2017), 252–274.

MR3556684 Matthes, Nils Ellipticdouble zeta values. J. Number Theory 171 (2017), 227–251.

MR3556683 Gras, Georges Nogeneral Riemann-Hurwitz formula for relative $p$-class groups. J.Number Theory 171 (2017), 213–226.

MR3556681 Xiao, Xuanxuan Higherintegral moments of automorphic $L$-functions in short intervals. J.Number Theory 171 (2017), 169–197.

MR3556680 Langlois,Marie-Andrée B. The valuative capacity of the set of sums of $d$-thpowers. J. Number Theory 171 (2017), 155–168.

MR3556679 van Ittersum,Jan-Willem M. A group-invariant version of Lehmer's conjectureon heights. J. Number Theory 171 (2017), 145–154.

MR3556678 Bibak,Khodakhast; Kapron, Bruce M.; Srinivasan,Venkatesh; Tauraso, Roberto; Tóth, LászlóRestrictedlinear congruences. J. Number Theory 171 (2017), 128–144.

MR3556677 Hu, Su; Kim, Min-Soo The $p$-adicanalytic Dedekind sums. J. Number Theory 171 (2017), 112–127.

MR3556676 Li, Zhonghua; Qin, Chen Shuffleproduct formulas of multiple zeta values. J. Number Theory 171(2017), 79–111.

MR3556675 Shparlinski,Igor E. On the convex hull of the points on multivariatemodular hyperbolas. J. Number Theory 171 (2017), 71–78.

MR3556674 Jiang, Yujiao; Lü, Guangshi Sumsof coefficients of $L$-functions and applications. J. NumberTheory 171 (2017), 56–70.

MR3556673 Sebe, GabrielaIleana A near-optimal solution to the Gauss-Kuzmin-Lévy problemfor $\theta$-expansions. J. Number Theory 171 (2017),43–55.

MR3556672 Lin, Bernard L.S. Congruences modulo 27 for cubic partition pairs. J.Number Theory 171 (2017), 31–42.

MR3556671 Araci, Serkan; Duran, Ugur; Acikgoz, Mehmet $(\rho,q)$-Volkenbornintegration. J. Number Theory 171 (2017), 18–30.

MR3556670 Xia, Ernest X.W.; Yao, Olivia X.M. Arithmetic properties for $(s,t)$-regular bipartitionfunctions.J. Number Theory 171 (2017), 1–17.

MR3556291 Bourgain, J. Decoupling,exponential sums and the Riemann zeta function. J. Amer. Math. Soc. 30(2017), no. 1, 205–224.

MR3556289 Frantzikinakis,Nikos; Host, Bernard Higherorder Fourier analysis of multiplicative functions and applications. J.Amer. Math. Soc. 30 (2017), no. 1, 67–157.

MR3554744 Cooper, Shaun; Kane, Ben; Ye, Dongxi Analoguesof the Ramanujan-Mordell theorem. J. Math. Anal. Appl. 446(2017), no. 1, 568–579.

MR3554732 Aistleitner,Christoph; Pańkowski,Łukasz Large values of L-functions from the Selberg class. J.Math. Anal. Appl. 446 (2017), no. 1, 345–364.

MR3554730 Cao, Zhu; Hu, Yong Onrational matrix exact covering systems of $\Bbb{Z}\sp n$ and itsapplications to Ramanujan's forty identities. J. Math. Anal. Appl. 446(2017), no. 1, 322–334.

MR3554719 Qiu, Song-Liang; Ma, Xiao-Yan; Huang, Ti-Ren Someproperties of the difference between the Ramanujan constant and beta function. J.Math. Anal. Appl. 446 (2017), no. 1, 114–129.

MR3548515 Özkan, E.; Geçer, A.; Altun, İ. Anew sequence realizing Lucas numbers, and the Lucas bound.Electron. J. Math.Anal. Appl. 5 (2017), no. 1, 148–154.

MR3562377 Folsom, Amanda Mockand mixed mock modular forms in the lower half-plane. Arch. Math.(Basel)107 (2016), no. 5, 487–498.

MR3562029 Sun, Zhi-Wei Ona pair of zeta functions. Int. J. Number Theory 12 (2016), no.8, 2323–2342.

MR3562028 Jhorar, Bablesh; Khanduja, SudeshK. On power basis of a class of algebraic number fields. Int.J. Number Theory 12 (2016), no. 8, 2317–2321.

MR3562027 Saad Eddin,Sumaia An explicit upper bound for $\vert L(1,\chi)\vert $ when $\chi(2)=1$ and$\chi$ iseven. Int. J. Number Theory 12 (2016), no. 8, 2299–2315.

MR3562026 Krumm, David Alocal-global principle in the dynamics of quadratic polynomials. Int.J. Number Theory 12 (2016), no. 8, 2265–2297.

MR3562025 Hertgen, Alan Splittingproperties of the reduction of semi-abelian varieties. Int. J. NumberTheory12 (2016), no. 8, 2241–2264.

MR3562024 Ivić, Aleksandar Onsome upper bounds for the zeta-function and the Dirichlet divisor problem. Int.J. Number Theory 12 (2016), no. 8, 2231–2239.

MR3562023 Zaman, Asif Onthe least prime ideal and Siegel zeros. Int. J. Number Theory 12(2016), no. 8, 2201–2229.

MR3562021 Sadek, Mohammad Charactersums, Gaussian hypergeometric series, and a family of hyperelliptic curves. Int.J. Number Theory 12 (2016), no. 8, 2173–2187.

MR3562020 Bibak,Khodakhast; Kapron, Bruce M.; Srinivasan,Venkatesh On a restricted linear congruence.Int. J. NumberTheory 12 (2016), no. 8, 2167–2171.

MR3562019 Väänänen, Keijo Algebraicindependence of certain Mahler numbers. Int. J. Number Theory 12(2016), no. 8, 2159–2166.

MR3562018 Pehlivan, Cihan Theaverage multiplicative order of a finitely generated subgroup of the rationalsmodulo primes. Int. J. Number Theory 12 (2016), no. 8,2147–2158.

MR3562017 Al-Shaghay,Abdullah; Dilcher, Karl Analoguesof the binomial coefficient theorems of Gauss and Jacobi. Int. J.Number Theory 12 (2016), no. 8, 2125–2145.

MR3562016 Zhang, Yichao Divisibilityproperties for weakly holomorphic modular forms with sign vectors. Int.J. Number Theory 12 (2016), no. 8, 2107–2123.

MR3562015 Blackwell, Sarah; Durham, Gabriel; Thompson,Katherine; Treece, Tiffany Ageneralization of a method of Mordell to ternary quadratic forms. Int.J. Number Theory 12 (2016), no. 8, 2081–2105.

MR3562014 Kim, Sungjin Onthe order of $a$ modulo $n$, on average. Int. J. NumberTheory 12 (2016), no. 8, 2073–2080.

MR3562013 Hamahata,Yoshinori Dedekind sums and the transformation formula infunction fields. Int. J. Number Theory 12 (2016), no. 8,2061–2072.

MR3562012 Zantout, Dania Cuspidalityin higher genus. Int. J. Number Theory 12 (2016), no. 8,2043–2060.

MR3561864 Bringmann,Kathrin; Kane, Ben Polarharmonic Maass forms and their applications. Abh. Math. Semin. Univ.Hambg. 86 (2016), no. 2, 213–233.

MR3561831 Wang, ZhangJie Congruentelliptic curves with non-trivial Shafarevich-Tate groups. Sci. ChinaMath. 59 (2016), no. 11, 2145–2166.

MR3561830 Cao, XiaoDong; Tanigawa, Yoshio; Zhai, WenGuang Tong-typeidentity and the mean square of the error term for an extended Selberg class. Sci.China Math. 59 (2016), no. 11, 2103–2144.

MR3559649 Falissard,Marie-Pierre Une approche intuitive des nombres hyperréels. (French)[An intuitive approach to hyperreal numbers] Quadrature No.101 (2016), 32–35.

MR3559646 Thomas, Gabriel Polynômeminimal d'un nombre algébrique. (French) [Minimal polynomial of analgebraic number] Quadrature No. 101 (2016), 22–27.

MR3559645 Morin, Claude Périodesde la suite de Fibonacci réduite. (French) [Periods of the reducedFibonacci sequence] Quadrature No. 101 (2016), 19–21.

MR3557126 Gu, Chao; Wang, Liuquan; Xia, Ernest X.W. Congruences modulo powers of 3 for generalized Frobeniusparitions with six colors. Acta Arith. 175 (2016), no. 3,291–300.

MR3557125 Sun, Zhi-Hong Somerelations between $t(a,b,c,d;n)$ and $N(a,b,c,d;n)$. ActaArith. 175 (2016), no. 3, 269–289.

MR3557124 Bugeaud, Yann; Schleischitz,Johannes On uniform approximation to real numbers. ActaArith. 175 (2016), no. 3, 255–268.

MR3557123 Jaulent,Jean-François Sur le radical kummérien des $\Bbb Z\sb \ell$-extensions. (French)[On the Kummer radical of $\Bbb Z\sb \ell$-extensions] Acta Arith. 175(2016), no. 3, 245–253.

MR3557122 Pomerance, Carl; Thompson, Lola; Weingartner,Andreas On integers $n$ for which $X\sp n-1$hasa divisor of every degree. Acta Arith. 175 (2016), no. 3,225–243.

MR3557120 He, Xiaoguang; Huang, Bingrong Exponentialsums involving the Möbius function. Acta Arith. 175 (2016),no. 3, 201–209.

MR3552747 Lagarias,Jeffrey C. Erdős, Klarner, and the $3x+1$ problem. Amer.Math. Monthly 123 (2016), no. 8, 753–776.

MR3536232 Dergach, P. S.; Aĭrapetov, è. S. Onthe progressive decomposition of a sequence of natural numbers with a gap oflength 2. (Russian) Intellekt. Sist. 20 (2016), no. 2,67–85.

MR3535552 Kodzokov, A. Kh.; Beslaneev, Z. O.; Nagorov, A. L.; Tkhamokov, M. B. Onlinear Diophantine equations and ways to solve them. (Russian) Vestn.KRAUNTS. Fiz.-Mat. Nauki 2016, no. 2(13), 18–23.

MR3557141 Filaseta,Michael; Rocks, Brady Onthe irreducibility of a polynomial associated with the strong factorialconjecture. Colloq. Math. 145 (2016), no. 2, 307–314.

MR3557132 Martinjak, Ivica; Urbiha, Igor Anew generalized Cassini determinant. Colloq. Math. 145 (2016),no. 2, 209–218.

MR3556498 Gonek, S. M.; Montgomery, H.L. Extreme values of the zeta function at critical points. Q.J. Math.67 (2016), no. 3, 483–505.

MR3556497 Bui, H. M.; Heap, Winston P.; Turnage-Butterbaugh,Caroline L. Gaps between zeros of Dedekind zeta-functions ofquadratic number fields. II. Q. J. Math. 67 (2016), no. 3,467–481.

MR3556494 Elsholtz,Christian Egyptian fractions with odd denominators. Q.J. Math. 67 (2016), no. 3, 425–430.

MR3554639 Iacò, Maria Rita; Steiner,Wolfgang; Tichy, Robert F. Linearrecursive odometers and beta-expansions. Unif. Distrib. Theory 11(2016), no. 1, 175–186.

MR3554638 Krčmarsky, David; Mišík, Ladislav; Václavíková,Zuzana On small sets of distribution functions of ratio blocksequences. Unif. Distrib. Theory 11 (2016), no. 1, 165–174.

MR3554637 Nair,Radhakrishnan; Nasr, Entesar Paircorrelations and random walks on the integers. Unif. Distrib. Theory 11(2016), no. 1, 159–164.

MR3554636 Mišík, Ladislav; Šustek, Jan; Volkmann, Bodo OnHausdorff dimensions related to sets with given asymptotic and gap densities. Unif.Distrib. Theory 11 (2016), no. 1, 141–157.

MR3554635 Verger-Gaugry,Jean-Louis On the conjecture of Lehmer, limit Mahler measure oftrinomials and asymptotic expansions. Unif. Distrib. Theory 11(2016), no. 1, 79–139.

MR3554634 De Koninck,Jean-Marie; Kátai, Imre; Phong, Bui Minh On strong normality. Unif.Distrib. Theory11 (2016), no. 1, 59–78.