Chebyshevskii Sbornik
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Chebyshevskii Sb.:
Year:
Volume:
Issue:
Page:
Find






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


Chebyshevskii Sb., 2020, Volume 21, Issue 4, Pages 9–18 (Mi cheb918)  

Stechkin's works in number theory

M. R. Gabdullin, S. V. Konyagin


Abstract: This paper is devoted to the analysis of S. B. Stechkin's contribution to some questions in analytic number theory. There are five areas of his research in the field of number theory. First, the works of S. B. Stechkin on the theory of the Riemann zeta function are considered. His results on even trigonometric polynomials played a role in these studies. Another area of research to which S. B. Stechkin made a significant contribution together with A. Y. Popov, relates to the asymptotic distribution of prime numbers on average. The third question, to which one of the works of S. B. Stechkin in analytic number theory was devoted, is related to Vinogradov’s mean value theorem, the main method for estimating Weyl sums. The fourth area of research, where S. B. Stechkin managed to get a result that could not be strengthened over the past 30 years, is the estimation of complete rational trigonometric sums. Finally, the fifth direction is the study of Gauss sums. Stechkin’s result in this direction and the problem he posed inspired followers to the present time.

Keywords: trigonometric sums, the Riemann zeta-function, distribution of prime numbers.

DOI: https://doi.org/10.22405/2226-8383-2018-21-4-9-18

Full text: PDF file (598 kB)

UDC: 511.33

Citation: M. R. Gabdullin, S. V. Konyagin, “Stechkin's works in number theory”, Chebyshevskii Sb., 21:4 (2020), 9–18

Citation in format AMSBIB
\Bibitem{1}
\by M.~R.~Gabdullin, S.~V.~Konyagin
\paper Stechkin's works in number theory
\jour Chebyshevskii Sb.
\yr 2020
\vol 21
\issue 4
\pages 9--18
\mathnet{http://mi.mathnet.ru/cheb918}
\crossref{https://doi.org/10.22405/2226-8383-2018-21-4-9-18}


Linking options:
  • http://mi.mathnet.ru/eng/cheb918
  • http://mi.mathnet.ru/eng/cheb/v21/i4/p9

    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
  • Number of views:
    This page:28
    Full text:2

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021