The second moment of quadratic twists of modular L-functions

被引：46

作者：

Soundararajan, K. ^{[1
]}

Young, Matthew P. ^{[2
]}

机构：

[1] Stanford Univ, Stanford, CA 94305 USA

[2] Texas A&M Univ, Dept Math, College Stn, TX 77843 USA

来源：

JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY | 2010年 / 12卷 / 05期

基金：

美国国家科学基金会;

关键词：

MEAN-VALUES;

D O I：

10.4171/JEMS/224

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the second moment of the central values of quadratic twists of a modular L-function. Unconditionally, we obtain a lower bound which matches the conjectured asymptotic formula, while on GRH we prove the asymptotic formula itself.

引用

页码：1097 / 1116

页数：20

共 35 条

[31] On positive real zeros of theta and L-functions associated with real, even and primitive characters [J].

Louboutin, Stephane R. ;

Munsch, Marc .

PUBLICATIONES MATHEMATICAE-DEBRECEN, 2013, 83 (04) :643-665

[32] Lower bounds for the moments of the derivatives of the riemann zeta-function and dirichlet L-functions [J].

Sono, Keiju .

LITHUANIAN MATHEMATICAL JOURNAL, 2012, 52 (04) :420-434

[33] Lower order terms for the one-level density of elliptic curve L-functions [J].

Huynh, D. K. ;

Keating, J. P. ;

Snaith, N. C. .

JOURNAL OF NUMBER THEORY, 2009, 129 (12) :2883-2902

[34] Spectralmoment formulae for GL(3) x GL(2) L-functions III: the twisted case [J].

Kwan, Chung-Hang .

MATHEMATISCHE ANNALEN, 2025, 391 (01) :363-398

[35] Value distribution for the derivatives of the logarithm of L-functions from the Selberg class in the half-plane of absolute convergence [J].

Nakamura, Takashi ;

Pankowski, Lukasz .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2016, 433 (01) :566-577

← 1 2 3 4 →