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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) Russian version article
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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
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. Math., 78:2 (2014), 293–353
Citation in format AMSBIB
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\paper A strengthening of a~theorem of Bourgain and Kontorovich
\jour Izv. Math.
\yr 2014
\vol 78
\issue 2
\pages 293--353
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  • 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
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    Abstract page:743
    Russian version PDF:225
    English version PDF:10
    References:78
    First page:41
     
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