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Izv. Akad. Nauk SSSR Ser. Mat., 1985, Volume 49, Issue 2, Pages 326–333 (Mi izv1357)  

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

On the zeros of the function $\zeta(s)$ in the neighborhood of the critical line

A. A. Karatsuba


Abstract: The following theorem is proved. If $H\geqslant T^a$, where $T>T_0>0$ and $a>27/82$, then for $1/2<\sigma\leqslant1$ the estimate
$$ N(\sigma,T+H)-N(\sigma,T)=O(\frac{H}{\sigma-0.5}) $$
holds uniformly in $\sigma$, where $N(\sigma_1,t)$ denotes the number of zeros $s=\sigma+it$, with $\sigma>\sigma_1$ and $0<t<T$, of the Riemann zeta-function $\zeta(s)$.
Bibliography: 4 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1986, 26:2, 307–313

Bibliographic databases:

UDC: 511
MSC: 11M26
Received: 29.11.1984

Citation: A. A. Karatsuba, “On the zeros of the function $\zeta(s)$ in the neighborhood of the critical line”, Izv. Akad. Nauk SSSR Ser. Mat., 49:2 (1985), 326–333; Math. USSR-Izv., 26:2 (1986), 307–313

Citation in format AMSBIB
\Bibitem{Kar85}
\by A.~A.~Karatsuba
\paper On~the zeros of the function $\zeta(s)$ in the neighborhood of the critical line
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1985
\vol 49
\issue 2
\pages 326--333
\mathnet{http://mi.mathnet.ru/izv1357}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=791306}
\zmath{https://zbmath.org/?q=an:0582.10027}
\transl
\jour Math. USSR-Izv.
\yr 1986
\vol 26
\issue 2
\pages 307--313
\crossref{https://doi.org/10.1070/IM1986v026n02ABEH001149}


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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, “The Riemann zeta function and its zeros”, Russian Math. Surveys, 40:5 (1985), 23–82  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. Z. Kh. Rakhmonov, “Estimate of the density of the zeros of the Riemann zeta function”, Russian Math. Surveys, 49:2 (1994), 168–169  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. A. A. Karatsuba, “On the function $S(t)$”, Izv. Math., 60:5 (1996), 901–931  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. 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
    5. Do Dyk Tam, “O kolichestve nulei dzeta-funktsii Rimana, lezhaschikh v «pochti vsekh» ochen korotkikh promezhutkakh okrestnosti kriticheskoi pryamoi”, Chebyshevskii sb., 17:3 (2016), 106–124  mathnet  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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