Pair correlation of zeros of the real and imaginary parts of the Riemann zeta-function

Steven M. Gonek; Haseo Ki

doi:10.1016/j.jnt.2017.10.024

Pair correlation of zeros of the real and imaginary parts of the Riemann zeta-function

Steven M. Gonek, Haseo Ki

Department of Mathematics

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

Abstract

We show that if the Riemann Hypothesis is true for the Riemann zeta-function, ζ(s), and 0<a<1/2, then all but a finite number of the zeros of ℜζ(a+it), ℑζ(a+it), and similar functions are simple. We also study the pair correlation of the zeros of these functions assuming the Riemann Hypothesis is true and 0<a≤1/2.

Original language	English
Pages (from-to)	35-61
Number of pages	27
Journal	Journal of Number Theory
Volume	186
DOIs	https://doi.org/10.1016/j.jnt.2017.10.024
Publication status	Published - 2018 May

Bibliographical note

Funding Information:
Research of the first author was partially supported by National Science Foundation grant DMS 1200582 . The first author also thanks Yonsei University and the Korea Institute for Advanced Study for their generous support and hospitality. Research of the second author was supported by a National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIP) (No. 2017R1A2B2002702 ).

Publisher Copyright:
© 2017 Elsevier Inc.

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1016/j.jnt.2017.10.024

Cite this

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abstract = "We show that if the Riemann Hypothesis is true for the Riemann zeta-function, ζ(s), and 0",

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Pair correlation of zeros of the real and imaginary parts of the Riemann zeta-function

Abstract

Bibliographical note

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