The fourth moment of quadratic Dirichlet L-functions over function fields

被引：33

作者：

Florea, Alexandra ^{[1
]}

机构：

[1] Stanford Univ, Dept Math, Stanford, CA 94305 USA

来源：

GEOMETRIC AND FUNCTIONAL ANALYSIS | 2017年 / 27卷 / 03期

关键词：

RANDOM-MATRIX THEORY; ZETA-FUNCTIONS; HYPERELLIPTIC CURVES; INTEGRAL MOMENTS; MEAN-VALUE; ZEROS;

D O I：

10.1007/s00039-017-0409-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We obtain an asymptotic formula for the fourth moment of quadratic Dirichlet L-functions over , as the base field is fixed and the genus of the family goes to infinity. According to conjectures of Andrade and Keating, we expect the fourth moment to be asymptotic to up to an error of size , where P is a polynomial of degree 10 with explicit coefficients. We prove an asymptotic formula with the leading three terms, which agrees with the conjectured result.

引用

页码：541 / 595

页数：55

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