TWISTS OF AUTOMORPHIC L-FUNCTIONS AT THE CENTRAL POINT

被引：1

作者：

Bui, H. M. ^{[1
]}

机构：

[1] Univ Zurich, Inst Math, CH-8057 Zurich, Switzerland

来源：

INTERNATIONAL JOURNAL OF NUMBER THEORY | 2013年 / 9卷 / 04期

基金：

瑞士国家科学基金会; 英国工程与自然科学研究理事会;

关键词：

Automorphic L-functions; nonvanishing; mollifier method; two-piece mollifier; DIRICHLET L-FUNCTIONS; HIGH DERIVATIVES; CENTRAL VALUES; ZETA-FUNCTION; ZEROS; RANK;

D O I：

10.1142/S1793042113500115

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the nonvanishing of twists of automorphic L-functions at the center of the critical strip. Given a primitive character chi modulo D satisfying some technical conditions, we prove that the twisted L-functions L(f. chi, s) do not vanish at s = 1/2 for a positive proportion of primitive forms of weight 2 and level q, for large prime q. We also investigate the central values of high derivatives of L(f. chi, s), and from that derive an upper bound for the average analytic rank of the studied L-functions.

引用

页码：1015 / 1053

页数：39

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