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Izv. Akad. Nauk SSSR Ser. Mat., 1984, Volume 48, Issue 6, Pages 1214–1224 (Mi izv1515)  

This article is cited in 15 scientific papers (total in 16 papers)

The distribution of zeros of the function $\zeta(1/2+it)$

A. A. Karatsuba


Abstract: The author proves two theorems of a metric character on the distribution of zeros of odd order of the Riemann zeta-function that lie on the critical line.
Bibliography: 5 titles.

Full text: PDF file (679 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Izvestiya, 1985, 25:3, 519–529

Bibliographic databases:

UDC: 511
MSC: Primary 10H05; Secondary 30C15
Received: 17.04.1984

Citation: A. A. Karatsuba, “The distribution of zeros of the function $\zeta(1/2+it)$”, Izv. Akad. Nauk SSSR Ser. Mat., 48:6 (1984), 1214–1224; Math. USSR-Izv., 25:3 (1985), 519–529

Citation in format AMSBIB
\Bibitem{Kar84}
\by A.~A.~Karatsuba
\paper The distribution of zeros of the function $\zeta(1/2+it)$
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1984
\vol 48
\issue 6
\pages 1214--1224
\mathnet{http://mi.mathnet.ru/izv1515}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=772113}
\zmath{https://zbmath.org/?q=an:0584.10019|0558.10033}
\transl
\jour Math. USSR-Izv.
\yr 1985
\vol 25
\issue 3
\pages 519--529
\crossref{https://doi.org/10.1070/IM1985v025n03ABEH001303}


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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. L. V. Kiseleva, “On the number of zeros of the function $\zeta(s)$ on “almost all” short intervals of the critical line”, Math. USSR-Izv., 32:3 (1989), 475–499  mathnet  crossref  mathscinet  zmath
    3. A. A. Karatsuba, “On the zeros of the Davenport–Heilbronn function lying on the critical line”, Math. USSR-Izv., 36:2 (1991), 311–324  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. A. A. Karatsuba, “Zeros of certain Dirichlet series”, Russian Math. Surveys, 45:1 (1990), 207–208  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    5. A. A. Karatsuba, “The distribution of prime numbers”, Russian Math. Surveys, 45:5 (1990), 99–171  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    6. A. A. Karatsuba, “On the number of zeros of the Riemann zeta-function lying in almost all short intervals of the critical line”, Russian Acad. Sci. Izv. Math., 40:2 (1993), 353–376  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    7. M. A. Korolev, “The argument of the Riemann zeta-function on the critical line”, Izv. Math., 67:2 (2003), 225–264  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    8. A. A. Karatsuba, “Zeros and Local Extrema of Trigonometric Sums”, Problems Inform. Transmission, 39:1 (2003), 78–91  mathnet  crossref  mathscinet  zmath
    9. 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
    10. S. A. Gritsenko, E. A. Karatsuba, M. A. Korolev, I. S. Rezvyakova, D. I. Tolev, M. E. Changa, “Scientific Achievements of Anatolii Alekseevich Karatsuba”, Proc. Steklov Inst. Math., 280, suppl. 2 (2013), S1–S22  mathnet  crossref  crossref  zmath  isi  elib
    11. A. A. Karatsuba, “Venskii doklad: o kolichestve nulei dzeta-funktsii Rimana na korotkikh promezhutkakh kriticheskoi pryamoi”, Chebyshevskii sb., 16:1 (2015), 19–31  mathnet  elib
    12. Do Dyk Tam, “Raspredelenie nulei, lezhaschikh na kriticheskoi pryamoi, lineinykh kombinatsii $L$-funktsii Dirikhle”, Chebyshevskii sb., 16:3 (2015), 183–208  mathnet  elib
    13. Do Dyk Tam, “O nulyakh dzeta-funktsii Rimana $\zeta(s)$, lezhaschikh na pochti vsekh korotkikh promezhutkakh kriticheskoi pryamoi”, Chebyshevskii sb., 17:1 (2016), 71–89  mathnet  elib
    14. 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
    15. A. A. Karatsuba, “On zeros of certain Dirichlet series”, Proc. Steklov Inst. Math., 296, suppl. 2 (2017), 6–10  mathnet  crossref  crossref  isi  elib
    16. M. A. Korolev, “On Anatolii Alekseevich Karatsuba's works written in the 1990s and 2000s”, Proc. Steklov Inst. Math., 299 (2017), 1–43  mathnet  crossref  crossref  isi  elib  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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