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Izv. RAN. Ser. Mat., 2005, Volume 69, Issue 4, Pages 75–88 (Mi izv648)  

This article is cited in 5 scientific papers (total in 5 papers)

Sign changes of the function $S(t)$ on short intervals

M. A. Korolev


Abstract: In this paper, we study sign changes of the function $S(t)$ on short intervals of the real line. It is proved that, for almost all values of $T$, there is a point at which $S(t)$ changes sign and whose distance from $T$ does not exceed $4.39\ln\ln\ln\ln T$.

DOI: https://doi.org/10.4213/im648

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English version:
Izvestiya: Mathematics, 2005, 69:4, 719–731

Bibliographic databases:

UDC: 511
MSC: 11L03, 11N37, 11M06, 11M26
Received: 28.04.2005

Citation: M. A. Korolev, “Sign changes of the function $S(t)$ on short intervals”, Izv. RAN. Ser. Mat., 69:4 (2005), 75–88; Izv. Math., 69:4 (2005), 719–731

Citation in format AMSBIB
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\paper Sign changes of the function $S(t)$ on short intervals
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\yr 2005
\vol 69
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\pages 75--88
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\pages 719--731
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  • https://doi.org/10.4213/im648
  • http://mi.mathnet.ru/eng/izv/v69/i4/p75

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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. A. A. Karatsuba, M. A. Korolev, “Behaviour of the argument of the Riemann zeta function on the critical line”, Russian Math. Surveys, 61:3 (2006), 389–482  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. Boyarinov R.N., “Izmenenie znaka funktsii $S(T)$ na korotkikh intervalakh”, Vestn. Mosk. un-ta. Ser. 1: Matem. Mekh., 2010, no. 3, 51–53  zmath  elib
    3. R. N. Boyarinov, “Argument dzeta-funktsii Rimana”, Chebyshevskii sb., 11:1 (2010), 54–67  mathnet  mathscinet
    4. R. N. Boyarinov, “Probabilistic methods in the theory of the Riemann zeta-function”, Theory Probab. Appl., 56:2 (2011), 181–192  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    5. Korolev M.A., “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
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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