# О показателе иррациональности числа $ln2$@@@On the Irrationality Exponent of the Number $ln2$

@inproceedings{2010,
title={О показателе иррациональности числа \$ln2\$@@@On the Irrationality Exponent of the Number \$ln2\$},
author={Юрий Валентинович Нестеренко and Yuri Valentinovich Nesterenko},
year={2010}
}
• Published 2010
• Mathematics
12 Citations
On the Irrationality Measures of Certain Numbers. II
For the irrationalitymeasures of the numbers $$\sqrt {2k - 1}$$2k−1 arctan$$\left( {\sqrt {2k - 1} /\left( {k - 1} \right)} \right)$$(2k−1/(k−1)), where k is an even positive integer, upper boundsExpand
On Catalan’S constant
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 speciallyExpand
Irrationality measure of the number
Using a new integral construction combining the idea of symmetry suggested by Salikhov in 2007 and the integral introduced by Marcovecchio in 2009, we obtain a new bound for the irrationality measureExpand
Symmetrized version of the Markovecchio integral in the theory of Diophantine approximations
• Mathematics
• 2015
A new integral construction unifying the idea of symmetry proposed by Salikhov in 2007 and the integral introduced by Markovecchio in 2009 is considered. The application of this construction leads,Expand
Quadratic irrationality exponents of certain numbers
The paper presents upper estimates for the non-quadraticity measure of the numbers $\sqrt {2k + 1} \ln ((k + 1 - \sqrt {2k + 1} /k)$ and $\sqrt {2k - 1} arctg(\sqrt {2k - 1} /(k - 1))$, where k ∈ ℕ.Expand

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The group structure for ζ(3)
• Mathematics
• 2001
1. Introduction. In his proof of the irrationality of ζ(3), Apéry [1] gave sequences of rational approximations to ζ(2) = π 2 /6 and to ζ(3) yielding the irrationality measures µ(ζ(2)) < 11.85078. ..Expand
Approximants de Padé et mesures effectives d’irrationalité
Les approximants de Pade; des fonctions hypergeometriques ont ete utilises pour l’etude en des points rationnels z=p/q des approximations diophantiennes des valeurs de ces fonctions. Cette methodeExpand
Number Theoretic Applications of Polynomials with Rational Coefficients Defined by Extremality Conditions
It is well known that classes of polynomials in one variable defined by various extremality conditions play an extremely important role in complex analysis. Among these classes we find orthogonalExpand