MR2016年4月份数论最新文献题录265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

MR2016年2月份数论最新文献题录254条 

MR2016年3月份数论最新文献题录230条

MR2016年4月份收录文献总量为10265条，其中数论研究最新文献题录265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

MR2016-04-265 for Number Theory.pdf

或者直接登录MathSciNet ®数据库进行浏览。 

MR3459064 Chen, Yong-Gao; Tang, Min On a generalization of a theorem ofSárközy and Sós. European J. Combin. 54 (2016), 201–206.

MR3459059 Mrazović, Rudi Extractors in Paley graphs: a randommodel. European J. Combin. 54 (2016), 154–162.

MR3457040 Liao, Qunying; Li, Jiyou; Pu, Keli On the existence for some specialprimitive elements in finite fields. Chin. Ann. Math. Ser. B 37 (2016), no. 2, 259–266.

MR3456887 Bourgain, Jean; Gamburd, Alexander; Sarnak, Peter Markoff triples and strongapproximation. C. R. Math. Acad. Sci. Paris 354 (2016), no. 2, 131–135.

MR3455618 Mignot, Teddy Points de hauteur bornée sur leshypersurfaces lisses des variétés toriques. (French) [Points of bounded height on smoothhypersurfaces of toric varieties] Acta Arith. 172 (2016), no. 1, 1–97.

MR3452683 Lim, Dongkyu; Qi, Feng On the Appell type λ-Changheepolynomials. J. Nonlinear Sci. Appl. 9 (2016), no. 4, 1872–1876.

MR3452672 Kang, Jung Yoog; Ryoo, Cheon Seoung A research on the some properties anddistribution of zeros for Stirling polynomials. J. Nonlinear Sci. Appl. 9 (2016), no. 4, 1735–1747.

MR3459537 Qu, Zhenhua A note on representation functions withdifferent weights. Colloq. Math. 143 (2016), no. 1, 105–112.

MR3459534 De Koninck, Jean-Marie; Kátai, Imre Shifted values of the largest primefactor function and its average value in short intervals. Colloq. Math. 143 (2016), no. 1, 39–62.

MR3459532 Zakarczemny, Maciej Number of solutions in a box of alinear equation in an Abelian group. Colloq. Math. 143 (2016), no. 1, 17–22.

MR3455758 Capuano, L.; Masser, D.; Pila, J.; Zannier, U. Rational points on Grassmannians andunlikely intersections in tori. Bull. Lond. Math. Soc. 48 (2016), no. 1, 141–154.

MR3455753 Le Boudec, Pierre Height of rational points on quadratictwists of a given elliptic curve. Bull. Lond. Math. Soc.48 (2016), no. 1, 99–108.

MR3455748 Vidaux, Xavier; Videla, Carlos R. A note on the Northcott property andundecidability. Bull. Lond. Math. Soc.48 (2016), no. 1, 58–62.

MR3455624 Pong, Wai Yan Applications of differential algebra toalgebraic independence of arithmetic functions. Acta Arith. 172 (2016), no. 2, 149–173.

MR3455623 Bérczes, Attila; Luca, Florian; Pink, István; Ziegler, Volker Finiteness results for Diophantinetriples with repdigit values. Acta Arith. 172 (2016), no. 2, 133–148.

MR3455622 Biró, András; Lapkova, Kostadinka The class number one problem for thereal quadratic fields Q((an)2+4a−−−−−−−−−√).Acta Arith. 172 (2016), no. 2, 117–131.

MR3455621 Nunes, Ramon M. On Bourgain's bound for shortexponential sums and squarefree numbers. Acta Arith. 172 (2016), no. 2, 99–116.

MR3455382 Zhao, Feng-Zhen The log-convexity of Genocchi numbersand the monotonicity of some sequences related to Genocchi numbers. J.Math. Inequal. 10(2016), no. 2, 541–550.

MR3455302 Al-Saket, Amal Some results for the zeros of a classof Fibonacci-type polynomials. J. Math. Inequal. 10 (2016), no. 1, 45–52.

MR3455281 Van Order, Jeanine Erratum: On the quaternionic p-adic L-functions associatedto Hilbert modular eigenforms [MR2926558]. Int.J. Number Theory 12(2016), no. 1, 305–311.

MR3455280 Leinonen, Leena; Leinonen, Marko; Matala-aho, Tapani On approximation measures of q-exponentialfunction.Int. J. Number Theory 12 (2016), no. 1, 287–303.

MR3455279 Hatley, Jeffrey Obstruction criteria for modulardeformation problems. Int. J. Number Theory 12 (2016), no. 1, 273–285.

MR3455278 Česnavičius, Kęstutis Local factors valued in normal domains. Int.J. Number Theory 12(2016), no. 1, 249–272.

MR3455277 Centeleghe, Tommaso Giorgio Integral Tatemodules and splitting of primes in torsion fields of elliptic curves.Int. J.Number Theory 12(2016), no. 1, 237–248.

MR3455275 Li, Taiyu Enlarged major arcs in theWaring-Goldbach problem. Int. J. Number Theory 12 (2016), no. 1, 205–217.

MR3455273 Dejou, Gaelle; Roblot, Xavier-François The GaloisBrumer-Stark conjecture for SL2(F3)-extensions. Int. J. Number Theory 12 (2016), no. 1, 165–188.

MR3455272 Sun, Zhi-Hong Cubic congruences and sums involving (3kk). Int. J.Number Theory 12(2016), no. 1, 143–164.

MR3455271 Jameson, Marie A problem of Zagier on quadratic polynomialsand continued fractions. Int. J. Number Theory12 (2016), no. 1, 121–141.

MR3455270 Zhang, Wenpeng; Han, Di A new identity involving the classicalKloosterman sums and 2-dimensional Kloosterman sums. Int. J. NumberTheory 12 (2016),no. 1, 111–119.

MR3455269 Lamzouri, Youness A bias in Mertens' product formula. Int.J. Number Theory 12(2016), no. 1, 97–109.

MR3455268 Girstmair, Kurt Congruences modulo 4 for thealternating sum of the partial quotients. Int. J. Number Theory12 (2016), no. 1, 93–96.

MR3455267 Lagarias, Jeffrey C.; Mehta, Harsh Products of binomial coefficients andunreduced Farey fractions. Int. J. Number Theory 12 (2016), no. 1, 57–91.

MR3455266 Gillespie, Timothy L.; Ye, Yangbo Zero correlation with lower-order termsfor automorphic L-functions. Int. J. Number Theory 12 (2016), no. 1, 27–55.

MR3455264 Alaca, Şaban; Kesicioğlu, Yavuz Evaluation of the convolution sums ∑l+27m=nσ(l)σ(m) and ∑l+32m=nσ(l)σ(m).Int. J. NumberTheory 12 (2016),no. 1, 1–13.

MR3453555 Cereceda, José Luis Explicit form of the Faulhaberpolynomials. College Math. J. 46 (2016), no. 5, 359–363.

MR3453549 Brown, Ezra Saints and scoundrels and two theoremsthat are really the same. College Math. J. 46 (2016), no. 5, 326–334.

MR3451584 Meguedmi, Djohra; Sebbar, Ahmed Faà di Bruno's formula and modularforms. Complex Anal. Oper. Theory 10 (2016), no. 2, 409–435.

MR3440107 Pratt, Kyle; Shakan, George; Zaharescu, Alexandru A generalization of theSchur-Siegel-Smyth trace problem.J. Math. Anal. Appl. 436 (2016), no. 1, 489–500.

MR3455132 Hirano, Miki; Ishii, Taku; Miyazaki, Tadashi The archimedean zeta integrals for GL(3)×GL(2). Proc. JapanAcad. Ser. A Math. Sci. 92(2016), no. 2, 27–32.

MR3453541 Gaitanas, Konstantinos A partialsolution of representing 1 as a sum of n distinct unitfractions. Amer. Math. Monthly 123 (2016), no. 1, 87.
MR3453536 Shivarajkumar Beyond Schur's conjecture. Amer.Math. Monthly 123(2016), no. 1, 66–70.

MR3454680 Murase, Atsushi; Narita, Hiro-aki Fourier expansion of Arakawa liftingII: Relation with central L-values.Internat. J. Math. 27 (2016), no. 1, 1650001, 32 pp.

MR3454375 Platt, D. J.; Trudgian, T. S. On the first sign change of θ(x)−x. Math. Comp. 85 (2016), no. 299, 1539–1547.

MR3454373 Grenié, Loïc; Molteni, Giuseppe Zeros of Dedekind zeta functions underGRH. Math. Comp. 85 (2016), no. 299, 1503–1522.

MR3454372 Jeon, Daeyeol Families of elliptic curves over cycliccubic number fields with prescribed torsion. Math. Comp.85 (2016), no. 299, 1485–1502.

MR3454371 Abatzoglou, Alexander; Silverberg, Alice; Sutherland, Andrew V.; Wong, Angela A framework for deterministic primalityproving using elliptic curves with complex multiplication. Math. Comp. 85 (2016), no. 299, 1461–1483.

MR3453368 Basak, Tathagata The complex Lorentzian Leech latticeand the bimonster (II). Trans. Amer. Math. Soc. 368 (2016), no. 6, 4171–4195.

MR3453360 Bilyk, Dmitriy; Ma, Xiaomin; Pipher, Jill; Spencer, Craig Diophantine approximations anddirectional discrepancy of rotated lattices. Trans. Amer. Math. Soc. 368 (2016), no. 6, 3871–3897.

MR3453986 Valentino, Maria On Euler characteristics of Selmergroups for abelian varieties over global function fields.Arch. Math. (Basel) 106 (2016), no. 2, 117–128.

MR3453847 Dudek, Adrian W.; Platt, David J. On the sum of the square of a prime anda square-free number. LMS J. Comput. Math. 19 (2016), no. 1, 16–24.

MR3453018 Janulis, Kęstutis; Jurgaitis, Donatas; Laurinčikas, Antanas; Macaitienė, Renata Universality theorems for somecomposite functions. Math. Model. Anal. 21 (2016), no. 1, 35–46.

MR3454090 de la Bretèche, Régis; Browning, Tim D.; Salberger, Per Counting rational points on the Cayleyruled cubic.Eur. J. Math. 2 (2016), no. 1, 55–72.

MR3453618 Ge, Wenxu; Li, Weiping One Diophantine inequality with unlikepowers of prime variables. J. Inequal. Appl.2016, 2016:33, 8 pp.

MR3453617 Xin, Lin Some identities related to Riemannzeta-function. J. Inequal. Appl. 2016, 2016:32, 6 pp.

MR3453387 Anglès, B.; Pellarin, F.; Tavares Ribeiro, F. Arithmetic of positive characteristic L-series values inTate algebras. With anappendix by F. Demeslay. Compos. Math. 152 (2016), no. 1, 1–61.

MR3453325 Qi, Feng Diagonal recurrence relations,inequalities, and monotonicity related to the Stirling numbers of the secondkind. Math. Inequal. Appl. 19 (2016), no. 1, 313–323.

MR3453321 Samadi, Saed; Nishihara, Akinori A class of continued fractioninequalities. Math. Inequal. Appl. 19 (2016), no. 1, 263–269.

MR3452950 Wang, Andrew Y. Z.; Zhang, Fan The reciprocal sums of the Fibonacci3-subsequences. Adv. Difference Equ.2016, 2016:27, 15 pp.

MR3452696 Adrian, Moshe; Liu, Baiying; Stevens, Shaun; Xu, Peng On the Jacquet conjecture on the localconverse problem for p-adic GLN. Represent.Theory 20 (2016),1–13.

MR3452168 Scott, Reese; Styer, Robert Number of solutions to ax+by=cz. Publ. Math.Debrecen 88 (2016),no. 1-2, 131–138.
MR3452166 Azizi, Abdelmalek; Taous, Mohammed; Zekhnini, Abdelkader On the 2-groups whose abelianizationsare of type (2,4) and applications. Publ. Math. Debrecen 88 (2016), no. 1-2, 93–117.

MR3452164 Cipu, Mihai; Filipin, Alan; Fujita, Yasutsugu Bounds for Diophantine quintuples II. Publ.Math. Debrecen 88(2016), no. 1-2, 59–78.

MR3452162 Paulin, Roland An explicit André-Oort type result for P1(C)×Gm(C) based onlogarithmic forms. Publ. Math. Debrecen 88 (2016), no. 1-2, 21–33.

MR3451942 Lü, Fan; Wu, Jun Diophantine analysis in beta-dynamicalsystems and Hausdorff dimensions. Adv. Math. 290 (2016), 919–937.

MR3451937 Cui, Su-Ping; Gu, Nancy S. S.; Huang, Anthony X. Congruence properties for a certain kindof partition functions. Adv. Math. 290 (2016), 739–772.

MR3451920 Choi, SoYoung; Kim, Chang Heon Weakly holomorphic Hecke eigenforms andHecke eigenpolynomials. Adv. Math. 290 (2016), 144–162.

MR3451919 Morris, Ian D. A rigorous version of R. P. Brent'smodel for the binary Euclidean algorithm. Adv. Math. 290 (2016), 73–143.

MR3446471 Koo, Namhun; Cho, Gook Hwa; Kwon, Soonhak On r-th root extractionalgorithm in Fq for q≡lrs+1(modrs+1) with 0<l<r and small s. IEEE Trans.Comput. 65 (2016),no. 1, 322–325.

MR3451399 Thorne, Jack A. Automorphy of some residually dihedralGalois representations. Math. Ann. 364 (2016), no. 1-2, 589–648.

MR3451383 Becher, Verónica; Bugeaud, Yann; Slaman, Theodore A. On simply normal numbers to differentbases. Math. Ann. 364 (2016), no. 1-2, 125–150.

MR3451364 Spearman, Blair K.; Yang, Qiduan; Yoo, Jeewon Minimal indices of pure cubic fields. Arch.Math. (Basel) 106(2016), no. 1, 35–40.

MR3451228 Becher, Verónica; Bugeaud, Yann; Slaman, Theodore A. The irrationality exponents ofcomputable numbers.Proc. Amer. Math. Soc. 144 (2016), no. 4, 1509–1521.

MR3451227 Fuselier, Jenny G.; McCarthy, Dermot Hypergeometric type identities in the p-adic setting andmodular forms.Proc. Amer. Math. Soc. 144 (2016), no. 4, 1493–1508.

MR3451223 Rolen, Larry A new construction of Eisenstein'scompletion of the Weierstrass zeta function. Proc. Amer. Math. Soc. 144 (2016), no. 4, 1453–1456.

MR3451222 Bringmann, Kathrin; Mertens, Michael H.; Ono, Ken p-adic properties ofmodular shifted convolution Dirichlet series. Proc. Amer. Math. Soc. 144 (2016), no. 4, 1439–1451.

MR3449237 Zywina, David The Sato-Tate law for Drinfeld modules. Trans.Amer. Math. Soc. 368(2016), no. 3, 2185–2222.

MR3451433 Delfs, Christina; Galbraith, Steven D. Computing isogenies betweensupersingular elliptic curves over Fp. Des. CodesCryptogr. 78 (2016),no. 2, 425–440.

MR3451350 Grishkov, A.; Logachev, D. Resultantal varieties related to zeroesof L-functionsof Carlitz modules. Finite Fields Appl. 38 (2016), 116–176.

MR3451347 Peterlongo, Pietro; Sala, Massimiliano; Tinnirello, Claudia A discrete logarithm-based approach tocompute low-weight multiples of binary polynomials. Finite Fields Appl. 38 (2016), 57–71.

MR3451346 Tosun, Cemile Explicit factorizations of generalizedDickson polynomials of order 2m via generalized cyclotomic polynomialsover finite fields. Finite Fields Appl. 38 (2016), 40–56.

MR3467514 Károlyi, Gyula A Lie algebra approach to differencesets: homage to Yahya Ould Hamidoune. Ann. Univ. Sci. Budapest. EötvösSect. Math. 57 (2014),75–81.

MR3449012 Cheng, Miranda C. N.; Duncan, John F. R.; Harvey, Jeffrey A. Umbral moonshine and the Niemeierlattices.Res. Math. Sci. 1 (2014), Art. 3, 81 pp.

MR3431861 Kamalinezhad, A. On the geometrization of the absoluteGalois group. (Russian) Fundam.Prikl. Mat. 18 (2013),no. 6, 145–159.

MR3431857 Golubev, K. V. A differential equation on the closurefunction of a hexagonal lattice by a trivalent tree.(Russian) Fundam. Prikl. Mat. 18 (2013), no. 6, 91–94.

MR3431854 Adrianov, N. M.; Zvonkin, A. K. Weighted trees with primitive edgerotation groups. (Russian) Fundam.Prikl. Mat. 18 (2013),no. 6, 5–50.