Sato-Tate equidistribution of certain families of Artin L-functions

TL;DR

This paper investigates the distribution of Artin L-functions associated with geometric families of number fields, identifying their Sato-Tate measures and symmetry types of low-lying zeros to understand their statistical properties.

Contribution

It determines the Sato-Tate measures and symmetry types for specific families of Artin L-functions linked to geometric parametrizations of number fields, advancing understanding of their zero distributions.

Findings

Identified Sato-Tate measures for various Artin L-function families

Determined the symmetry types of low-lying zeros

Enhanced understanding of the statistical behavior of these L-functions

Abstract

We study various families of Artin $L$-functions attached to geometric parametrizations of number fields. In each case we find the Sato-Tate measure of the family and determine the symmetry type of the distribution of the low-lying zeros.