On large gaps between consecutive zeros, on the critical line, of some Dirichlet $L$-functions

TL;DR

This paper demonstrates the existence of significantly large gaps between consecutive zeros on the critical line of certain Dirichlet L-functions, specifically for even primitive characters, highlighting notable irregularities in zero distribution.

Contribution

It establishes the existence of large gaps between zeros of Dirichlet L-functions on the critical line, a novel result in understanding their zero distribution.

Findings

Large gaps are at least 3.54 times the average gap

Gaps occur between zeros on the critical line of Dirichlet L-functions

Focus on functions with even primitive characters

Abstract

This text shows the existence of large (3.54 times the average) gaps between consecutive zeros, on the critical line, of some Dirichlet $L$-functions $L(s,\chi),$ with $\chi$ being an even primitive Dirichlet character.