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Izvestiya: Mathematics, 2015, Volume 79, Issue 2, Pages 288–310
DOI: https://doi.org/10.1070/IM2015v079n02ABEH002743 (Mi im8253) 		 
This article is cited in 12 scientific papers (total in 12 papers)

A strengthening of a theorem of Bourgain and Kontorovich. III

I. D. Kan

Moscow Aviation Institute (State University of Aerospace Technologies)
English version PDF (427 kB) Citations (12)
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DOI: https://doi.org/10.1070/IM2015v079n02ABEH002743
Abstract: We prove that the set of positive integers contains a positive proportion of denominators of the finite continued fractions all of whose partial quotients belong to the alphabet $\{1,2,3,4,10\}$. The corresponding theorem was previousy known only for the alphabet $\{1,2,3,4,5\}$ and for alphabets of larger cardinality.
Keywords: continued fraction, continuant, trigonometric sum, Zaremba's conjecture.
Funding agency Grant number
Russian Foundation for Basic Research 12-01-00681-a
The research was financially supported by RFBR (grant no. 12-01-00681-a).
Received: 16.05.2014
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2015, Volume 79, Issue 2, Pages 77–100
DOI: https://doi.org/10.4213/im8253
Bibliographic databases:
Document Type: Article
UDC: 511.321+511.31
MSC: Primary 11J70; Secondary 11A55, 11L07
Language: English
Original paper language: Russian
Citation: I. D. Kan, “A strengthening of a theorem of Bourgain and Kontorovich. III”, Izv. RAN. Ser. Mat., 79:2 (2015), 77–100; Izv. Math., 79:2 (2015), 288–310
Citation in format AMSBIB
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    Cycle of papers
    This publication is cited in the following 12 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:587
    Russian version PDF:169
    English version PDF:11
    References:80
    First page:37
     
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