Matematicheskie Zametki
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
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

Matematicheskie Zametki, 2021, Volume 109, Issue 3, Pages 452–463
DOI: https://doi.org/10.4213/mzm11326 (Mi mzm11326) 		 
Local Discrepancies in the Problem of the Distribution of the Sequence $\{k\alpha\}$

A. V. Shutov

Vladimir State University
Full-text PDF (500 kB)
References:
PDF
HTML
DOI: https://doi.org/10.4213/mzm11326
Abstract: The paper deals with local discrepancies in the problem of the distribution of the sequence $\{k\alpha\}$, i.e., the remainder terms in asymptotic formulas for the number of points in this sequence lying in prescribed intervals. The construction of intervals for which local discrepancies tend to infinity slower than any given function is presented. Moreover, it is shown that there exists an uncountable set of such intervals. Previously, similar results were obtained only for irrationalities with bounded partial quotients of their continued fraction expansions.
Keywords: uniform distribution, local discrepancies, inhomogeneous Diophantine approximations, continued fractions.
Received: 28.07.2016
Revised: 06.10.2020
English version:
Mathematical Notes, 2021, Volume 109, Issue 3, Pages 473–482
DOI: https://doi.org/10.1134/S0001434621030147
Bibliographic databases:
Document Type: Article
UDC: 511.43
Language: Russian
Citation: A. V. Shutov, “Local Discrepancies in the Problem of the Distribution of the Sequence $\{k\alpha\}$”, Mat. Zametki, 109:3 (2021), 452–463; Math. Notes, 109:3 (2021), 473–482
Citation in format AMSBIB
\Bibitem{Shu21}
\by A.~V.~Shutov
\paper Local Discrepancies in the Problem of the Distribution of the Sequence~$\{k\alpha\}$
\jour Mat. Zametki
\yr 2021
\vol 109
\issue 3
\pages 452--463
\mathnet{http://mi.mathnet.ru/mzm11326}
\crossref{https://doi.org/10.4213/mzm11326}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4223931}
\elib{https://elibrary.ru/item.asp?id=46948370}
\transl
\jour Math. Notes
\yr 2021
\vol 109
\issue 3
\pages 473--482
\crossref{https://doi.org/10.1134/S0001434621030147}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000670513100014}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85113167652}
Linking options:
  • https://www.mathnet.ru/eng/mzm11326
  • https://doi.org/10.4213/mzm11326
  • https://www.mathnet.ru/eng/mzm/v109/i3/p452
    • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
    Statistics & downloads:
    Abstract page:185
    Full-text PDF :21
    References:24
    First page:12
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024