《山东大学学报(理学版)》 ›› 2022, Vol. 57 ›› Issue (2): 72-77.doi: 10.6040/j.issn.1671-9352.0.2021.603
• • 上一篇
刘灿
LIU Can
摘要： 令k表示偶整数, f(z)为全模群Γ=SL2(Z)上权重为k的本原全纯尖形式。λsym2 f ×sym3f(n)表示Rankin-Selberg L-函数L(s,sym2f ×sym3f )的Dirichlet级数的第n个系数。利用Newton-Thorne对L(s,sym jf )在j上的突破性工作,研究λ2sym2 f ×sym3f(n)的均值分布情况,得到一个较为精确的渐近公式。
中图分类号:
| [1] DELIGNE P. La conjecture de Weil. I[J]. Institut des Hautes Études Scientifiques. Publications Mathématiques, 1974, 43:273-307. [2] HECKE E. Theorie der eisensteinschen reihen höherer stufe und ihre anwendung auf funktionentheorie und arithmetik[J]. Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 1927, 5(1):199-224. [3] FOMENKO O M. Identities involving the coefficients of automorphic L-functions[J]. Journal of Mathematical Sciences, 2006, 133(6):1749-1755. [4] FOMENKO O M. Mean value theorems for automorphic L-functions[J]. Algebra i Analiz, 2007, 19(5):246-264. [5] TANG H C. Estimates for the Fourier coefficients of symmetric square L-functions[J]. Archiv der Mathematik, 2013, 100(2):123-130. [6] HE X G. Integral power sums of Fourier coefficients of symmetric square L-functions[J]. Proceedings of the American Mathematical Society, 2019, 147(7):2847-2856. [7] RANKIN R A. Contributions to the theory of Ramanujans function τ(n) and similar arithemtical functions: I. The zeros of the function ∑∞n=1τ(n)/ns on the line Rs=13/2. II. The order of the Fourier coefficients of the integral modular forms[J]. Proceedings of the Cambridge Philosophical Society, 1939, 35:351-372. [8] SELBERG A. Bemerkungen über eine dirichletsche reihe, die mit der theorie der modulformen nahe verbunden ist[J]. Archiv for Mathematik og Naturvidenskab, 1940, 43:47-50. [9] LÜ G S, SANKARANARAYANAN A. On the coefficients of triple product L-functions[J]. The Rocky Mountain Journal of Mathematics, 2017, 47(2):553-570. [10] LIU H F. Mean value estimates of the coefficients of product L-functions[J]. Acta Mathematica Hungarica, 2018, 156(1):102-111. [11] LIU H F, ZHANG R. Some problems involving Hecke eigenvalues[J]. Acta Mathematica Hungarica, 2019, 159(1):287-298. [12] NEWTON J, THORNE J A. Symmetric power functoriality for holomorphic modular forms[J/OL]. [2019-12-24] (2021-08-25). https://arxiv.org/abs/1912.11261v3 [13] BOURGAIN J. Decoupling, exponential sums and the Riemann zeta function[J]. Journal of the American Mathematical Society, 2017, 30(1):205-224. [14] IVIC A. Exponent pairs and the zeta function of Riemann[J]. Studia Sci Math Hungar, 1980, 15(1/3):157-181. [15] NUNES R M. On the subconvexity estimate for self-dual GL(3)L-functions in the t-aspect[J/OL].[2017-3-13] (2020-11-28). https://arxiv.org/abs/1703.04424v1 [16] PERELLI A. General L-functions[J]. Annali di Matematica Pura ed Applicata, 1982, 130(4):287-306. |
| [1] | 李亭亭,劳会学. 一类混合型数论函数的均值估计[J]. 山东大学学报（理学版）, 2017, 52(8): 70-74. |
|
||
