SIMULTANEOUS NON-VANISHING FOR DIRICHLET L-FUNCTIONS

被引：11

作者：

Zacharias, Raphael ^{[1
]}

机构：

[1] Ecole Polytech Fed Lausanne, Mathgeom TAN, Stn 8, C-1015 Lausanne, Switzerland

来源：

ANNALES DE L INSTITUT FOURIER | 2019年 / 69卷 / 04期

关键词：

Modular forms; L-functions; trace functions; bilinear forms; twisted Kloost-erman sums; AUTOMORPHIC L-FUNCTIONS; SELBERG L-FUNCTIONS; SUBCONVEXITY PROBLEM; KLOOSTERMAN SUMS; TWISTS; BOUNDS; FORMS;

D O I：

10.5802/aif.3275

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We extend the work of Fouvry, Kowalski and Michel on correlation between Hecke eigenvalues of modular forms and algebraic trace functions in order to establish an asymptotic formula for a generalized cubic moment of modular L-functions at the central point s = 1/2 As an application, we exploit our recent result on the mollification of the fourth moment of Dirichlet L-functions to derive that for any pair (omega(1), omega(2)) of multiplicative characters modulo a prime q, there is a positive proportion of chi (mod q) such that the central values L(chi, 1/2), L(chi omega(1), 1/2) and L(chi omega(2), 1/2) are simultaneously not too small.

引用

页码：1459 / 1524

页数：66

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