Mean values of derivatives of L-functions in function fields: I

被引：10

作者：

Andrade, Julio ^{[1
]}

Rajagopal, Surajit ^{[2
]}

机构：

[1] Univ Exeter, Dept Math, N Pk Rd, Exeter EX4 4QF, Devon, England

[2] Univ Oxford, Math Inst, Radcliffe Observ Quarter, Woodstock Rd, Oxford OX2 6GG, England

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2016年 / 443卷 / 01期

基金：

英国工程与自然科学研究理事会;

关键词：

Function fields; Hyperelliptic curves; Derivatives of L-functions; Moments of L-functions; Quadratic Dirichlet L-functions; Random matrix theory; RIEMANN ZETA-FUNCTION; L(1/2; CHI);

D O I：

10.1016/j.jmaa.2016.05.019

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate the first moment of the second derivative of quadratic Dirichlet L-functions over the rational function field. We establish an asymptotic formula when the cardinality of the finite field is fixed and the genus of the hyperelliptic curves associated to a family of Dirichlet L-functions over F-q(T) tends to infinity. As a more general result, we compute the full degree three polynomial in the asymptotic expansion of the first moment of the second derivative of this particular family of L-functions. (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：526 / 541

页数：16

共 14 条

[1] The mean value of L(1/2, χ) in the hyperelliptic ensemble [J].