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., 2019, Volume 20, Issue 3, Pages 282–295 (Mi cheb812)  

On a version of Hadamard's method in the theory of Dirichlet's $L$-functions

O. V. Kolpakova, O. V. Popov, V. N. Chubarikov

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: In the paper a new version of the Hadamard's method in the theory of Dirichlet's $L$-functions is given. We prove of this method of the absence of the $L$-functions zeroes on the unit line. We show that the Hadamard's method allow to get results, which on the accuracy correspond to the Vallee Poussin results in the asymptotical law of the distribution of primes. Of this we extend possibilities of the Hadamard's method. New estimations of the zeta-sum twisted together with the Dirichlet's character by modulo, equals to the degree of an odd prime number are obtained that permits to get the modern limit of zeroes for the corresponding Dirichlet's $L$-function.

Keywords: Dirichlet's characters, the Hadamard's method, the asymptotical law of the distribution of primes with the Vallee Poussin remainder, Dirichlet's functions, the zeta-sum twisted together with the Dirichlet's character.

DOI: https://doi.org/10.22405/2226-8383-2018-20-3-282-295

Full text: PDF file (665 kB)

UDC: 511.3
Received: 24.09.2019
Accepted:12.11.2019

Citation: O. V. Kolpakova, O. V. Popov, V. N. Chubarikov, “On a version of Hadamard's method in the theory of Dirichlet's $L$-functions”, Chebyshevskii Sb., 20:3 (2019), 282–295

Citation in format AMSBIB
\Bibitem{KolPopChu19}
\by O.~V.~Kolpakova, O.~V.~Popov, V.~N.~Chubarikov
\paper On a version of Hadamard's method in the theory of Dirichlet's $L$-functions
\jour Chebyshevskii Sb.
\yr 2019
\vol 20
\issue 3
\pages 282--295
\mathnet{http://mi.mathnet.ru/cheb812}
\crossref{https://doi.org/10.22405/2226-8383-2018-20-3-282-295}


Linking options:
  • http://mi.mathnet.ru/eng/cheb812
  • http://mi.mathnet.ru/eng/cheb/v20/i3/p282

    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:12
    Full text:7

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