Small gaps between zeros of twisted L-functions

TL;DR

Assuming the Generalized Riemann Hypothesis, the paper proves the existence of many Dirichlet L-functions with pairs of zeros closer than 0.37 times their average spacing, using the asymptotic large sieve method.

Contribution

The paper introduces bounds for small zero gaps in families of twisted L-functions, extending previous results with a new analytical approach.

Findings

Existence of many small zero gaps under GRH

Bound of 0.37 times the average spacing for small gaps

Application of the asymptotic large sieve to zero spacing analysis

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.