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Uspekhi Mat. Nauk, 1985, Volume 40, Issue 5(245), Pages 19–70 (Mi umn2762)  

This article is cited in 16 scientific papers (total in 17 papers)

The Riemann zeta function and its zeros

A. A. Karatsuba


Full text: PDF file (3923 kB)
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English version:
Russian Mathematical Surveys, 1985, 40:5, 23–82

Bibliographic databases:

UDC: 517.5
MSC: 11M41, 11M20, 11M36, 11L03
Received: 18.11.1984

Citation: A. A. Karatsuba, “The Riemann zeta function and its zeros”, Uspekhi Mat. Nauk, 40:5(245) (1985), 19–70; Russian Math. Surveys, 40:5 (1985), 23–82

Citation in format AMSBIB
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\by A.~A.~Karatsuba
\paper The Riemann zeta function and its zeros
\jour Uspekhi Mat. Nauk
\yr 1985
\vol 40
\issue 5(245)
\pages 19--70
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\transl
\jour Russian Math. Surveys
\yr 1985
\vol 40
\issue 5
\pages 23--82
\crossref{https://doi.org/10.1070/RM1985v040n05ABEH003682}
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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. 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
    2. 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
    3. A. A. Karatsuba, “The distribution of prime numbers”, Russian Math. Surveys, 45:5 (1990), 99–171  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. A. A. Karatsuba, “On the zeros of a special type of function connected with Dirichlet series”, Math. USSR-Izv., 38:3 (1992), 471–502  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    5. 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
    6. A. A. Karatsuba, “On the zeros of arithmetic Dirichlet series without Euler product”, Russian Acad. Sci. Izv. Math., 43:2 (1994), 193–203  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    7. A. A. Karatsuba, “Fractional Moments and Zeros of $\zeta (s)$ on the Critical Line”, Math. Notes, 72:4 (2002), 466–472  mathnet  crossref  crossref  mathscinet  zmath  isi
    8. A. A. Karatsuba, M. A. Korolev, “The argument of the Riemann zeta function”, Russian Math. Surveys, 60:3 (2005), 433–488  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    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. Do Dyk Tam, “Raspredelenie nulei, lezhaschikh na kriticheskoi pryamoi, lineinykh kombinatsii $L$-funktsii Dirikhle”, Chebyshevskii sb., 16:3 (2015), 183–208  mathnet  elib
    12. 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
    13. S. A. Gritsenko, “On the Zeros of the Davenport–Heilbronn Function Lying on the Critical Line”, Math. Notes, 101:1 (2017), 166–170  mathnet  crossref  crossref  mathscinet  isi  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. S. A. Gritsenko, “On the zeros of the Davenport–Heilbronn function”, Proc. Steklov Inst. Math., 296 (2017), 65–87  mathnet  crossref  crossref  mathscinet  isi  elib
    17. S. A. Gritsenko, “O drobnykh momentakh uspokoennykh $L$-funktsii Lirikhle”, Chebyshevskii sb., 18:4 (2017), 168–187  mathnet  crossref
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