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Izv. RAN. Ser. Mat., 2010, Volume 74, Issue 4, Pages 83–118 (Mi izv2766)  

This article is cited in 12 scientific papers (total in 12 papers)

Gram's law and Selberg's conjecture on the distribution of zeros of the Riemann zeta function

M. A. Korolev

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: We prove a number of new assertions related to the zeros of the Riemann zeta function $\zeta(s)$ and to the so-called Gram law.

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

DOI: https://doi.org/10.4213/im2766

Full text: PDF file (668 kB)
References: PDF file   HTML file

English version:
Izvestiya: Mathematics, 2010, 74:4, 743–780

Bibliographic databases:

Document Type: Article
UDC: 511
MSC: 11M26, 11M06
Received: 07.02.2008

Citation: M. A. Korolev, “Gram's law and Selberg's conjecture on the distribution of zeros of the Riemann zeta function”, Izv. RAN. Ser. Mat., 74:4 (2010), 83–118; Izv. Math., 74:4 (2010), 743–780

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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 Gram's law in the theory of the Riemann zeta function”, Izv. Math., 76:2 (2012), 275–309  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. M. A. Korolev, “On Karatsuba's problem related to Gram's law”, Proc. Steklov Inst. Math., 276 (2012), 156–166  mathnet  crossref  mathscinet  isi
    3. R. N. Boyarinov, “On the number of Gram's intervals containing the ordinates of successive zeros of the Riemann zeta function”, Discrete Math. Appl., 22:5-6 (2012), 683–692  mathnet  crossref  crossref  mathscinet  elib
    4. 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
    5. 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
    6. 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
    7. Kargin V., “On fluctuations of Riemann's zeta zeros”, Probab. Theory Relat. Fields, 2013  crossref  mathscinet  isi  scopus
    8. 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
    9. M. A. Korolev, “On small values of the Riemann zeta-function at Gram points”, Sb. Math., 205:1 (2014), 63–82  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    10. M. A. Korolev, “Moments of trigonometric polynomials and their applications in the theory of the Riemann zeta-function”, Dokl. Math., 89:3 (2014), 305–307  mathnet  crossref  crossref  mathscinet  mathscinet  zmath  isi  elib  scopus
    11. 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
    12. M. A. Korolev, “Gram's Law in the Theory of Riemann Zeta-Function. Part 2”, Proc. Steklov Inst. Math., 294, suppl. 1 (2016), 1–78  mathnet  crossref  crossref  mathscinet  isi  elib  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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