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 Tr. Mat. Inst. Steklova, 2016, Volume 292, Pages 159–176 (Mi tm3695)

On Catalan's constant

Yu. V. Nesterenko

Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia

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-îôè-ì This work was supported in part by the Russian Foundation for Basic Research, project no. 13-01-12420-ofi-m.

DOI: https://doi.org/10.1134/S0371968516010106

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English version:
Proceedings of the Steklov Institute of Mathematics, 2016, 292, 153–170

Bibliographic databases:

UDC: 517.521.15

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, Tr. 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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