Small gaps between zeros of twisted L-functions
Number Theory
2012-02-14 v1
Abstract
We use the asymptotic large sieve, developed by the authors, to prove that if the Generalized Riemann Hypothesis is true, then there exist many Dirichlet L-functions that have a pair of consecutive zeros closer together than 0.37 times their average spacing. More generally, we investigate zero spacings within the family of twists by Dirichlet characters of a fixed L-function and give precise bounds for small gaps which depend only on the degree of the L-function.
Cite
@article{arxiv.1202.2671,
title = {Small gaps between zeros of twisted L-functions},
author = {J. B. Conrey and H. Iwaniec and K. Soundararajan},
journal= {arXiv preprint arXiv:1202.2671},
year = {2012}
}
Comments
19 pages; to appear in Acta Arithmetica