Izvestiya: Mathematics
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
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

Izvestiya: Mathematics, 2014, Volume 78, Issue 2, Pages 293–353
DOI: https://doi.org/10.1070/IM2014v078n02ABEH002689 (Mi im8032) 		 
This article is cited in 16 scientific papers (total in 16 papers)

A strengthening of a theorem of Bourgain and Kontorovich

I. D. Kana, D. A. Frolenkovb

a M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b Steklov Mathematical Institute of the Russian Academy of Sciences
English version PDF (737 kB) Citations (16)
References:
PDF
HTML
DOI: https://doi.org/10.1070/IM2014v078n02ABEH002689
Abstract: We prove that the set of positive integers contains a positive proportion of numbers satisfying Zaremba's conjecture with $A=7$. This result strengthens a similar theorem of Bourgain and Kontorovich obtained for $A=50$.
Keywords: continued fraction, continuant, exponential sums.
Funding agency Grant number
Russian Foundation for Basic Research 12-01-00681-а
11-01-00759-а
12-01-31165
Dynasty Foundation
Received: 10.07.2012
Revised: 24.05.2013
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2014, Volume 78, Issue 2, Pages 87–144
DOI: https://doi.org/10.4213/im8032
Bibliographic databases:
Document Type: Article
UDC: 511.321+511.31
MSC: 11A55, 11B05, 11P55
Language: English
Original paper language: Russian
Citation: I. D. Kan, D. A. Frolenkov, “A strengthening of a theorem of Bourgain and Kontorovich”, Izv. RAN. Ser. Mat., 78:2 (2014), 87–144; Izv. Math., 78:2 (2014), 293–353
Citation in format AMSBIB
\Bibitem{KanFro14}
\by I.~D.~Kan, D.~A.~Frolenkov
\paper A strengthening of a~theorem of Bourgain and Kontorovich
\jour Izv. RAN. Ser. Mat.
\yr 2014
\vol 78
\issue 2
\pages 87--144
\mathnet{http://mi.mathnet.ru/im8032}
\crossref{https://doi.org/10.4213/im8032}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3234819}
\zmath{https://zbmath.org/?q=an:06301842}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2014IzMat..78..293K}
\elib{https://elibrary.ru/item.asp?id=21826411}
\transl
\jour Izv. Math.
\yr 2014
\vol 78
\issue 2
\pages 293--353
\crossref{https://doi.org/10.1070/IM2014v078n02ABEH002689}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000338994500004}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84899527583}
Linking options:
  • https://www.mathnet.ru/eng/im8032
  • https://doi.org/10.1070/IM2014v078n02ABEH002689
  • https://www.mathnet.ru/eng/im/v78/i2/p87
    Cycle of papers
    This publication is cited in the following 16 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
    Statistics & downloads:
    Abstract page:733
    Russian version PDF:221
    English version PDF:8
    References:71
    First page:41
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024