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On Catalan’S constant

  • Yu. V. Nesterenko
Article
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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.

Keywords

STEKLOV Institute Prime Number Rational Approximation Hypergeometric Function Arithmetic Operation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Pleiades Publishing, Ltd. 2016

Authors and Affiliations

  1. 1.Faculty of Mechanics and MathematicsMoscow State UniversityMoscowRussia

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