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

JOURNAL OF NUMBER THEORY

卷:132

Article

Andrade, J. C.¹  Keating, J. P.¹ 

[1] Univ Bristol, Sch Math, Bristol BS8 1TW, Avon, England

关键词: Moments of quadratic Dirichlet L-functions;    Finite fields;    Function fields;    Random Matrix Theory;    Hyperelliptic curves;   

DOI  :  10.1016/j.jnt.2012.05.017

来源: Elsevier

【 摘 要 】

We obtain an asymptotic formula for the first moment of quadratic Dirichlet L-functions over the rational function field at the central point s = 1/2. Specifically, we compute the expected value of L(1/2, chi) for an ensemble of hyperelliptic curves of genus g over a fixed finite field as g -> infinity. Our approach relies on the use of the analogue of the approximate functional equation for such L-functions. The results presented here are the function field analogues of those obtained previously by Jutila in the number-field setting and are consistent with recent general conjectures for the moments of L-functions motivated by Random Matrix Theory. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free