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Mat. Sb., 2014, Volume 205, Number 1, Pages 67–86 (Mi msb8253)  

This article is cited in 1 scientific paper (total in 1 paper)

On small values of the Riemann zeta-function at Gram points

M. A. Korolev

Steklov Mathematical Institute of the Russian Academy of Sciences

Abstract: In this paper, we prove the existence of a large set of Gram points $t_{n}$ such that the values $\zeta(0.5+it_{n})$ are ‘anomalously’ close to zero. A lower bound for the negative ‘discrete’ moment of the Riemann zeta-function on the critical line is also given.
Bibliography: 13 titles.

Keywords: Riemann zeta-function, Hardy's function, Gram points.

Funding Agency Grant Number
Russian Foundation for Basic Research 12-01-31165-мол-а


DOI: https://doi.org/10.4213/sm8253

Full text: PDF file (580 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2014, 205:1, 63–82

Bibliographic databases:

Document Type: Article
UDC: 511.331
MSC: 11M06
Received: 10.06.2013 and 07.10.2013

Citation: M. A. Korolev, “On small values of the Riemann zeta-function at Gram points”, Mat. Sb., 205:1 (2014), 67–86; Sb. Math., 205:1 (2014), 63–82

Citation in format AMSBIB
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\pages 63--82
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  • https://doi.org/10.4213/sm8253
  • http://mi.mathnet.ru/eng/msb/v205/i1/p67

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. J. Kalpokas, P. Šarka, “Small values of the Riemann zeta function on the critical line”, Acta Arith., 169:3 (2015), 201–220  crossref  mathscinet  zmath  isi  elib  scopus
  • Математический сборник Sbornik: Mathematics (from 1967)
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