Probability Surveys

Statistical properties of zeta functions’ zeros

Vladislav Kargin

Full-text: Open access

Abstract

The paper reviews existing results about the statistical distribution of zeros for three main types of zeta functions: number-theoretical, geometrical, and dynamical. It provides necessary background and some details about the proofs of the main results.

Article information

Source
Probab. Surveys, Volume 11 (2014), 121-160.

Dates
First available in Project Euclid: 3 July 2014

Permanent link to this document
https://projecteuclid.org/euclid.ps/1404393850

Digital Object Identifier
doi:10.1214/13-PS214

Mathematical Reviews number (MathSciNet)
MR3264556

Zentralblatt MATH identifier
1301.11063

Subjects
Primary: 11M26: Nonreal zeros of $\zeta (s)$ and $L(s, \chi)$; Riemann and other hypotheses 11M50: Relations with random matrices 62E20: Asymptotic distribution theory

Keywords
Riemann’s zeta Selberg’s zeta Ruelle’s zeta Montgomery’s conjecture distribution of zeros

Citation

Kargin, Vladislav. Statistical properties of zeta functions’ zeros. Probab. Surveys 11 (2014), 121--160. doi:10.1214/13-PS214. https://projecteuclid.org/euclid.ps/1404393850


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