An estimate of the second moment of a sampling of the Riemann zeta function on the critical line

Sihun Jo; Minsuk Yang

doi:10.1016/j.jmaa.2014.01.040

An estimate of the second moment of a sampling of the Riemann zeta function on the critical line

Sihun Jo, Minsuk Yang

Department of Mathematics

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

Abstract

We investigate the second moment of a random sampling ζ(1/2+iX_t) of the Riemann zeta function on the critical line. Our main result states that if X_t is an increasing random sampling with gamma distribution, then for all sufficiently large t,E|ζ(1/2+iXt)|2=logt+O(logtloglogt).

Original language	English
Pages (from-to)	121-134
Number of pages	14
Journal	Journal of Mathematical Analysis and Applications
Volume	415
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2014.01.040
Publication status	Published - 2014 Jul 1

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

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10.1016/j.jmaa.2014.01.040

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abstract = "We investigate the second moment of a random sampling ζ(1/2+iXt) of the Riemann zeta function on the critical line. Our main result states that if Xt is an increasing random sampling with gamma distribution, then for all sufficiently large t,E|ζ(1/2+iXt)|2=logt+O(logtloglogt).",

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An estimate of the second moment of a sampling of the Riemann zeta function on the critical line

Abstract

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