Conjectures for the integral moments and ratios of \(L\)-functions over function fields
type: Item
instance of: scholarly article
title: Conjectures for the integral moments and ratios of \(L\)-functions over function fields
zbMATH Open document ID: 1318.11083
published in: Journal of Number Theory
publication date: 2014-08-29T00:00:00Z
full work available at URL: https://arxiv.org/abs/1407.3099
review text: \textit{J. B. Conrey} et al. [Proc. Lond. Math. Soc. (3) 91, No. 1, 33--104 (2005; Zbl 1075.11058); J. Number Theory 128, No. 6, 1516--1554 (2008; Zbl 1141.11040)] made two conjectures for the integral moments and ratios of \(L\)-functions defined over number fields. In this paper, the authors develop the function field analogues of these conjectures for the family of quadratic Dirichlet \(L\)-functions associated with hyperelliptic curves of genus \(g\) over a fixed finite field \(\mathbb{F}_q\). Specifically, the authors give a heuristic for the moments and ratios of the family of quadratic Dirichlet \(L\)-functions associated with hyperelliptic curves of genus \(g\) over a fixed finite field \(\mathbb{F}_q\) in the limit as \(g\rightarrow \infty\). Like in the number field case, the author observe that there is a striking resemblance to the corresponding formulae for the characteristic polynomials of random matrices. As an application, the authors calculate the one-level density for the zeros of these \(L\)-functions.
reviewed by: Rupam Barman
Mathematics Subject Classification ID: 11G20
Mathematics Subject Classification ID: 11M50
Mathematics Subject Classification ID: 14G10
zbMATH DE Number: 6335915
zbMATH Keywords: moments of quadratic Dirichlet
zbMATH Keywords: \(L\)-functions
zbMATH Keywords: ratios of \(L\)-functions
zbMATH Keywords: function fields
zbMATH Keywords: random matrix theory
zbMATH Keywords: hyperelliptic curves
author: J. C. Andrade
author: J. P. Keating
MaRDI profile type: Publication
OpenAlex ID: W2090082281
Wikidata QID: Q57937578
arXiv ID: 1407.3099
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DOI: 10.1016/J.JNT.2014.02.019
description: scientific article; zbMATH DE number 6335915