Low lying zeros of families of L-functions
Number Theory
2009-09-25 v1
Abstract
In Iwaniec-Sarnak [IS] the percentages of nonvanishing of central values of families of GL_2 automorphic L-functions was investigated. In this paper we examine the distribution of zeros which are at or neat s=1/2 (that is the central point) for such families of L-functions. Unlike [IS], most of the results in this paper are conditional, depending on the Generalized Riemann Hypothesis (GRH). It is by no means obvious, but on the other hand not surprising, that this allows us to obtain sharper results on nonvanishing.
Keywords
Cite
@article{arxiv.math/9901141,
title = {Low lying zeros of families of L-functions},
author = {Henryk Iwaniec and Wenzhi Luo and Peter Sarnak},
journal= {arXiv preprint arXiv:math/9901141},
year = {2009}
}
Comments
Abstract added in migration (from introduction)