On the Distribution of Zeroes of Artin-Schreier L-functions

TL;DR

This paper investigates the zero distribution of Artin-Schreier L-functions, analyzing zero counts in short intervals and comparing findings with predictions from a random matrix model.

Contribution

It provides new partial results on zero distributions in Artin-Schreier L-functions, aligning with random matrix theory predictions.

Findings

Zeroes distribution matches random unitary matrix model predictions

Partial results on zero counts in short intervals

Supports conjectural links between L-functions and random matrices

Abstract

We study the distribution of the zeroes of the L-functions of curves in the Artin-Schreier family. We consider the number of zeroes in short intervals and obtain partial results which agree with a random unitary matrix model.