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Low-lying zeros of quadratic Dirichlet L-functions: A transition in the ratios conjecture

Journal article
Authors D. Fiorilli
J. Parks
Anders Södergren
Published in Quarterly Journal of Mathematics
Volume 69
Issue 4
Pages 1129-1149
ISSN 0033-5606
Publication year 2018
Published at Department of Mathematical Sciences, Algebra and Geometry
Pages 1129-1149
Language en
Links dx.doi.org/10.1093/qmath/hay018
Subject categories Mathematical Analysis

Abstract

We study the 1-level density of low-lying zeros of quadratic Dirichlet L-functions by applying the L-functions Ratios Conjecture. We observe a transition in the main term as was predicted by the Katz-Sarnak heuristic as well as in the lower-order terms when the support of the Fourier transform of the corresponding test function reaches the point 1. Our results are consistent with those obtained in previous work under GRH and are furthermore analogous to results of Rudnick in the function field case.

Page Manager: Webmaster|Last update: 9/11/2012
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