Local Statistics for Zeros of Artin-Schreier L-functions

2021/07/05 by Alexei Entin, Entin, Alexei, Noam Pirani +1
Mathematics · #11M38 #11M50 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2107.02131

openalex publication_date 2021/07/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the local statistics of zeros of L-functions attached to Artin-Scheier curves over finite fields. We consider three families of Artin-Schreier L-functions: the ordinary, polynomial (the p-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.

Citations

• Lower Order Terms for Expected Value of Traces of Frobenius of a Family\n of Cyclic Covers of \ℙ¹_ mathbbF_q and One-Level Densities

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