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



Mat. Zametki:
Year:
Volume:
Issue:
Page:
Find






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


Mat. Zametki, 2011, Volume 89, Issue 4, Pages 530–546 (Mi mz9097)  

New Estimates of the Remainder in an Asymptotic Formula in the Multidimensional Dirichlet Divisor Problem

O. V. Kolpakova

M. V. Lomonosov Moscow State University

Abstract: We obtain a new value of the Karatsuba constant in the multidimensional Dirichlet divisor problem. We also find a new value of the exponent of the main parameter in the estimate of the mean value of the remainder in a given asymptotics. The proof of the main statements is based on the derivation of a new estimate of the Carleson abscissa in the theory of the Riemann zeta function.

Keywords: Dirichlet divisor problem, Riemann zeta function, Karatsuba constant, Carleson exponent, Dirichlet series

DOI: https://doi.org/10.4213/mzm9097

Full text: PDF file (492 kB)
References: PDF file   HTML file

English version:
Mathematical Notes, 2011, 89:4, 504–518

Bibliographic databases:

UDC: 511.335
Received: 28.12.2009

Citation: O. V. Kolpakova, “New Estimates of the Remainder in an Asymptotic Formula in the Multidimensional Dirichlet Divisor Problem”, Mat. Zametki, 89:4 (2011), 530–546; Math. Notes, 89:4 (2011), 504–518

Citation in format AMSBIB
\Bibitem{Kol11}
\by O.~V.~Kolpakova
\paper New Estimates of the Remainder in an Asymptotic Formula in the Multidimensional Dirichlet Divisor Problem
\jour Mat. Zametki
\yr 2011
\vol 89
\issue 4
\pages 530--546
\mathnet{http://mi.mathnet.ru/mz9097}
\crossref{https://doi.org/10.4213/mzm9097}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2856745}
\transl
\jour Math. Notes
\yr 2011
\vol 89
\issue 4
\pages 504--518
\crossref{https://doi.org/10.1134/S0001434611030229}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000290038700022}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79955587321}


Linking options:
  • http://mi.mathnet.ru/eng/mz9097
  • https://doi.org/10.4213/mzm9097
  • http://mi.mathnet.ru/eng/mz/v89/i4/p530

    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
  • Математические заметки Mathematical Notes
    Number of views:
    This page:279
    Full text:92
    References:43
    First page:21

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