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

Sihun Jo, Minsuk Yang

Research output: Contribution to journalArticle

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).

Original languageEnglish
Pages (from-to)121-134
Number of pages14
JournalJournal of Mathematical Analysis and Applications
Volume415
Issue number1
DOIs
Publication statusPublished - 2014 Jul 1

Fingerprint

Random Sampling
Riemann zeta function
Sampling
Moment
Line
Gamma distribution
Estimate

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Cite this

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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. / Jo, Sihun; Yang, Minsuk.

In: Journal of Mathematical Analysis and Applications, Vol. 415, No. 1, 01.07.2014, p. 121-134.

Research output: Contribution to journalArticle

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