LOCAL STATISTICS FOR ZEROS OF ARTIN-SCHREIER L-FUNCTIONS

Alexei Entin; Noam Pirani

doi:https://doi.org/10.1090/tran/8850

LOCAL STATISTICS FOR ZEROS OF ARTIN-SCHREIER L-FUNCTIONS

Alexei Entin, Noam Pirani

School of Mathematical Sciences

Tel Aviv University

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	6141-6175
Number of pages	35
Journal	Transactions of the American Mathematical Society
Volume	376
Issue number	9
DOIs	https://doi.org/10.1090/tran/8850
State	Published - 2023

All Science Journal Classification (ASJC) codes

Applied Mathematics
General Mathematics

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title = "LOCAL STATISTICS FOR ZEROS OF ARTIN-SCHREIER L-FUNCTIONS",

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.",

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note = "Publisher Copyright: {\textcopyright} 2023 American Mathematical Society.",

year = "2023",

doi = "https://doi.org/10.1090/tran/8850",

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N2 - 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.

AB - 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.

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U2 - https://doi.org/10.1090/tran/8850

DO - https://doi.org/10.1090/tran/8850

M3 - مقالة

SN - 0002-9947

VL - 376

SP - 6141

EP - 6175

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 9

ER -

LOCAL STATISTICS FOR ZEROS OF ARTIN-SCHREIER L-FUNCTIONS

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