Tr. Mat. Inst. Steklova, 2016, Volume 292, Pages 159–176
On Catalan's constant
Yu. V. Nesterenko
Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia
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.
|Russian Foundation for Basic Research
|This work was supported in part by the Russian Foundation for Basic Research, project no. 13-01-12420-ofi-m.
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Proceedings of the Steklov Institute of Mathematics, 2016, 292, 153–170
Received: January 15, 2015
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
\paper On Catalan's constant
\inbook Algebra, geometry, and number theory
\bookinfo Collected papers. Dedicated to Academician Vladimir Petrovich Platonov on the occasion of his 75th birthday
\serial Tr. Mat. Inst. Steklova
\publ MAIK Nauka/Interperiodica
\jour Proc. Steklov Inst. Math.
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