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 Probability Surveys > Vol. 11 (2014) open journal systems 


Statistical properties of zeta functions' zeros

Vladislav Kargin


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.

AMS 2000 subject classifications: 11M26, 11M50, 62E20.

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

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Kargin, Vladislav, Statistical properties of zeta functions' zeros, Probability Surveys, 11, (2014), 121-160 (electronic). DOI: 10.1214/13-PS214.

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