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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2016, Volume 292, Pages 159–176
DOI: https://doi.org/10.1134/S0371968516010106 (Mi tm3695) 		 
This article is cited in 3 scientific papers (total in 3 papers)

On Catalan's constant

Yu. V. Nesterenko

Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia
Full-text PDF (251 kB) Citations (3)
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DOI: https://doi.org/10.1134/S0371968516010106
Abstract: A new efficient construction of Diophantine approximations to Catalan's constant is presented that is based on the direct analysis of the representation of a hypergeometric function with specially chosen half-integer parameters as a series and as a double Euler integral over the unit cube. This allows one to significantly simplify the proofs of Diophantine results available in this domain and substantially extend the capabilities of the method. The sequences of constructed rational approximations are not good enough to prove irrationality, but the results established allow one to compare the quality of various constructions.
Funding agency Grant number
Russian Foundation for Basic Research 13-01-12420-офи-м
This work was supported in part by the Russian Foundation for Basic Research, project no. 13-01-12420-ofi-m.
Received: January 15, 2015
English version:
Proceedings of the Steklov Institute of Mathematics, 2016, Volume 292, Pages 153–170
DOI: https://doi.org/10.1134/S0081543816010107
Bibliographic databases:
Document Type: Article
UDC: 517.521.15
Language: Russian
Citation: Yu. V. Nesterenko, “On Catalan's constant”, Algebra, geometry, and number theory, Collected papers. Dedicated to Academician Vladimir Petrovich Platonov on the occasion of his 75th birthday, Trudy Mat. Inst. Steklova, 292, MAIK Nauka/Interperiodica, Moscow, 2016, 159–176; Proc. Steklov Inst. Math., 292 (2016), 153–170
Citation in format AMSBIB
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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