Small first zeros of L-functions

TL;DR

This paper extends previous results on the lowest zeros of L-functions with unitary symmetry to other families, analyzing how symmetry types influence the height of the first zeros.

Contribution

It generalizes the understanding of low-lying zeros across different L-function families based on their symmetry types.

Findings

Extended results to various symmetry types of L-functions.

Identified how symmetry influences the height of the first zero.

Provided a unified framework for low-lying zero statistics.

Abstract

From a family of L-functions with unitary symmetry, Hughes and Rudnick obtained results on the height of its lowest zero. We extend their results to other families of Lfunctions according to the type of symmetry coming from statistics for low-lying zeros.