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Izv. RAN. Ser. Mat., 2008, Volume 72, Issue 2, Pages 91–104 (Mi izv2636)  

This article is cited in 3 scientific papers (total in 4 papers)

On large distances between consecutive zeros of the Riemann zeta-function

M. A. Korolev

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: We obtain a new estimate for the number of zeros $\rho_n=\beta_n+i\gamma_n$ of the Riemann zeta-function, $14<\gamma_1<\gamma_2<…\le\gamma_n\le\gamma_{n+1}\le\cdots$, whose ordinates $\gamma_n$ belong to a given interval and for which the difference $\gamma_{n+r}-\gamma_n$ is sufficiently large in comparison with the ‘mean’ value $2\pi r(\ln\frac{\gamma_n}{2\pi})^{-1}$.

DOI: https://doi.org/10.4213/im2636

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English version:
Izvestiya: Mathematics, 2008, 72:2, 291–304

Bibliographic databases:

Document Type: Article
UDC: 511
MSC: 11M06, 11M26
Received: 20.03.2007

Citation: M. A. Korolev, “On large distances between consecutive zeros of the Riemann zeta-function”, Izv. RAN. Ser. Mat., 72:2 (2008), 91–104; Izv. Math., 72:2 (2008), 291–304

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    Erratum

    This publication is cited in the following articles:
    1. R. N. Boyarinov, “On large distances between neighbouring zeros of the Riemann zeta-function”, Discrete Math. Appl., 20:4 (2010), 411–420  mathnet  crossref  crossref  mathscinet  elib  elib
    2. R. N. Boyarinov, “Argument dzeta-funktsii Rimana”, Chebyshevskii sb., 11:1 (2010), 54–67  mathnet  mathscinet
    3. M. A. Korolev, “Letter to the editors”, Izv. Math., 75:4 (2011), 869–869  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. 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
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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