Conjectures for the integral moments and ratios of L-functions over function fields

JOURNAL OF NUMBER THEORY

卷:142

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;    Ratios of L-functions;    Finite fields;    Function fields;    Random matrix theory;    Hyperelliptic curves;   

DOI  :  10.1016/j.jnt.2014.02.019

来源: Elsevier

【 摘 要 】

We extend to the function field setting the heuristic previously developed, by Conrey, Farmer, Keating, Rubinstein and Snaith, for the integral moments and ratios of L-functions defined over number fields. Specifically, we give a heuristic for the moments and ratios of a family of L-functions associated with hyperelliptic curves of genus g over a fixed finite field F-q in the limit as g -> infinity. Like in the number field case, there is a striking resemblance to the corresponding formulae for the characteristic polynomials of random matrices. As an application, we calculate the one-level density for the zeros of these L-functions. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free