# On the irrationality exponent of the number ln 2

@article{Nesterenko2010OnTI,
title={On the irrationality exponent of the number ln 2},
author={Yu. V. Nesterenko},
journal={Mathematical Notes},
year={2010},
volume={88},
pages={530-543}
}
• Y. Nesterenko
• Published 9 November 2010
• Mathematics
• Mathematical Notes
We propose another method of deriving the Marcovecchio estimate for the irrationality measure of the number ln 2 following, for the most part, the method of proof of the irrationality of the number ζ(3) proposed by the author in 1996. The proof uses single complex integrals, the so-called Meyer G-functions, and is much simpler than that of Marcovecchio.
The paper presents upper estimates for the irrationality measure and the non-quadraticity measure for the numbers $\alpha_k=\sqrt{2k+1}\ln\frac{\sqrt{2k+1}-1}{\sqrt{2k+1}+1}, \ k\in\mathbb N.$
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.
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 measure
AbstractWe consider a new approach to estimating the irrationality measure of numbers that are values of the Gauss hypergeometric function. Some of the previous results are improved, in particular,
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 bounds
• Y. Nesterenko
• Mathematics
Proceedings of the Steklov Institute of Mathematics
• 2016
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
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
• Mathematics
Mathematical Notes
• 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,
• 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,

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