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Izv. RAN. Ser. Mat., 2012, Volume 76, Issue 2, Pages 67–102 (Mi izv5558)  

This article is cited in 6 scientific papers (total in 6 papers)

On Gram's law in the theory of the Riemann zeta function

M. A. Korolev

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: We prove an assertion of Selberg concerning Gram's rule and the distribution of zeros of the Riemann zeta function. We also prove some equivalent assertions.

Keywords: Gram's law, Gram's rule, argument of the Riemann zeta function.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation МК-4052.2009.1


DOI: https://doi.org/10.4213/im5558

Full text: PDF file (652 kB)
References: PDF file   HTML file

English version:
Izvestiya: Mathematics, 2012, 76:2, 275–309

Bibliographic databases:

Document Type: Article
UDC: 511.331
MSC: 11M06, 11M26
Received: 22.10.2010
Revised: 28.02.2011

Citation: M. A. Korolev, “On Gram's law in the theory of the Riemann zeta function”, Izv. RAN. Ser. Mat., 76:2 (2012), 67–102; Izv. Math., 76:2 (2012), 275–309

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  • http://mi.mathnet.ru/eng/izv5558
  • https://doi.org/10.4213/im5558
  • http://mi.mathnet.ru/eng/izv/v76/i2/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. M. A. Korolev, “On Selberg formulae related to Gram's law”, Sb. Math., 203:12 (2012), 1808–1816  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. Korolev M.A., “On some new results related to Gram's law”, Dokl. Math., 86:2 (2012), 661–662  mathnet  crossref  mathscinet  zmath  isi  elib  elib  scopus
    3. Korolev M., “Gram's law and the argument of the Riemann zeta function”, Publ. Inst. Math.-Beograd, 92:106 (2012), 53–78  crossref  mathscinet  zmath  isi  scopus
    4. M. A. Korolev, “On new results related to Gram's law”, Izv. Math., 77:5 (2013), 917–940  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    5. M. A. Korolev, “On large values of the Riemann zeta-function on short segments of the critical line”, Acta Arith., 166:4 (2014), 349–390  crossref  mathscinet  zmath  isi  scopus
    6. M. A. Korolev, “Large values of the Riemann zeta-function on short intervals of the critical line”, Dokl. Math., 91:1 (2015), 102–104  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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