Local Statistics for Zeros of Artin-Schreier L-functions
Number Theory
2022-11-18 v2
Abstract
We study the local statistics of zeros of -functions attached to Artin-Scheier curves over finite fields. We consider three families of Artin-Schreier -functions: the ordinary, polynomial (the -rank 0 stratum) and odd-polynomial families. We compute the 1-level zero-density of the first and third families and the 2-level density of the second family for test functions with Fourier transform supported in a suitable interval. In each case we obtain agreement with a unitary or symplectic random matrix model.
Keywords
Cite
@article{arxiv.2107.02131,
title = {Local Statistics for Zeros of Artin-Schreier L-functions},
author = {Alexei Entin and Noam Pirani},
journal= {arXiv preprint arXiv:2107.02131},
year = {2022}
}