On fluctuations of Riemann's zeta zeros

V. Kargin

doi:10.1007/s00440-012-0465-9

On fluctuations of Riemann's zeta zeros

V. Kargin

Mathematics and Statistics

Binghamton University

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

1 Scopus citations

Abstract

It is shown that the normalized fluctuations of Riemann's zeta zeros around their predicted locations follow the Gaussian law. It is also shown that fluctuations of two zeros, γ_k and γ_k+x with x ~ (log k)^β, β > 0, for large k follow the two-variate Gaussian distribution with correlation (1 - β)₊.

Original language	English
Pages (from-to)	575-604
Number of pages	30
Journal	Probability Theory and Related Fields
Volume	157
Issue number	3-4
DOIs	https://doi.org/10.1007/s00440-012-0465-9
State	Published - Dec 2013

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title = "On fluctuations of Riemann's zeta zeros",

abstract = "It is shown that the normalized fluctuations of Riemann's zeta zeros around their predicted locations follow the Gaussian law. It is also shown that fluctuations of two zeros, γk and γk+x with x \textasciitilde{} (log k)β, β > 0, for large k follow the two-variate Gaussian distribution with correlation (1 - β)+.",

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N2 - It is shown that the normalized fluctuations of Riemann's zeta zeros around their predicted locations follow the Gaussian law. It is also shown that fluctuations of two zeros, γk and γk+x with x ~ (log k)β, β > 0, for large k follow the two-variate Gaussian distribution with correlation (1 - β)+.

AB - It is shown that the normalized fluctuations of Riemann's zeta zeros around their predicted locations follow the Gaussian law. It is also shown that fluctuations of two zeros, γk and γk+x with x ~ (log k)β, β > 0, for large k follow the two-variate Gaussian distribution with correlation (1 - β)+.

UR - https://www.scopus.com/pages/publications/84888300097

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DO - 10.1007/s00440-012-0465-9

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VL - 157

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EP - 604

JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

IS - 3-4

ER -

On fluctuations of Riemann's zeta zeros

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