RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Izv. RAN. Ser. Mat.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Izv. RAN. Ser. Mat., 2003, Volume 67, Issue 2, Pages 21–60 (Mi izv426)  

This article is cited in 10 scientific papers (total in 10 papers)

The argument of the Riemann zeta-function on the critical line

M. A. Korolev


Abstract: We prove a new density theorem for the zeros of the Riemann zeta-function in the critical strip, and apply it to the problem of the number of sign changes of the argument of the zeta-function on almost all short intervals of the critical line.

DOI: https://doi.org/10.4213/im426

Full text: PDF file (2063 kB)
References: PDF file   HTML file

English version:
Izvestiya: Mathematics, 2003, 67:2, 225–264

Bibliographic databases:

UDC: 511
MSC: 11M06
Received: 24.09.2002

Citation: M. A. Korolev, “The argument of the Riemann zeta-function on the critical line”, Izv. RAN. Ser. Mat., 67:2 (2003), 21–60; Izv. Math., 67:2 (2003), 225–264

Citation in format AMSBIB
\Bibitem{Kor03}
\by M.~A.~Korolev
\paper The argument of the Riemann zeta-function on the critical line
\jour Izv. RAN. Ser. Mat.
\yr 2003
\vol 67
\issue 2
\pages 21--60
\mathnet{http://mi.mathnet.ru/izv426}
\crossref{https://doi.org/10.4213/im426}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1972992}
\zmath{https://zbmath.org/?q=an:1066.11038}
\elib{http://elibrary.ru/item.asp?id=13713727}
\transl
\jour Izv. Math.
\yr 2003
\vol 67
\issue 2
\pages 225--264
\crossref{https://doi.org/10.1070/IM2003v067n02ABEH000426}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000185541900002}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-27844588244}


Linking options:
  • http://mi.mathnet.ru/eng/izv426
  • https://doi.org/10.4213/im426
  • http://mi.mathnet.ru/eng/izv/v67/i2/p21

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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, “The argument of the Riemann zeta function”, Russian Math. Surveys, 60:3 (2005), 433–488  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. M. A. Korolev, “On large values of the function $S(t)$ on short intervals”, Izv. Math., 69:1 (2005), 113–122  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    3. M. A. Korolev, “Sign changes of the function $S(t)$ on short intervals”, Izv. Math., 69:4 (2005), 719–731  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    4. M. A. Korolev, “On multiple zeros of the Riemann zeta function”, Izv. Math., 70:3 (2006), 427–446  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    5. 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
    6. Korolev M.A., “On large distances between neighboring zeros of the Riemann zeta function”, Dokl. Math., 76:3 (2007), 940–943  mathnet  crossref  mathscinet  zmath  isi  elib  elib  scopus
    7. M. A. Korolev, “On large distances between consecutive zeros of the Riemann zeta-function”, Izv. Math., 72:2 (2008), 291–304  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    8. M. A. Korolev, “Gram's law and Selberg's conjecture on the distribution of zeros of the Riemann zeta function”, Izv. Math., 74:4 (2010), 743–780  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    9. V. Kargin, “On fluctuations of Riemann’s zeta zeros”, Probab. Theory Relat. Fields, 157:3-4 (2013), 575  crossref  mathscinet  zmath  isi  scopus
    10. 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 Российской академии наук. Серия математическая Izvestiya: Mathematics
    Number of views:
    This page:524
    Full text:150
    References:31
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020