# The Rhin-Viola method for log 2

@article{Marcovecchio2009TheRM,
title={The Rhin-Viola method for log 2},
author={Raffaele Marcovecchio},
journal={Acta Arithmetica},
year={2009},
volume={139},
pages={147-184}
}
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#### References

SHOWING 1-10 OF 18 REFERENCES
Austria E-mail: marcovr8@univie.ac.at Received on 1.12
• 2008
Diophantine approximations of log 2 and other logarithms
We describe a new approach to estimating μ(log 2), without improving Rukhadze’s result (1987). We find estimates for approximations to the number log 2 by numbers from the field ℚ(√2), to the numberExpand
The permutation group method for the dilogarithm
• Mathematics
• 2005
We give qualitative and quantitative improvements on all the best pre- viously known irrationality results for dilogarithms of positive rational numbers. We obtain such improvements by applying ourExpand
Approximation measures for logarithms of algebraic numbers
• Mathematics
• 2001
Given a number field K and a number ) lll we say that A > 0 is a K-irrationality measure of 03BE if, for any e > 0, > - ( 1 + e) p h(o) for all p E K with sufficiently large Weil logarithmic heightExpand
Irrationalité d’une infinité de valeurs de la fonction zêta aux entiers impairs
• Mathematics
• 2001
Au contraire des nombres ζ(2n)=∑k≥1 1/k2n= (−1)n−122n−1 B2nπ2n/(2n)! (n ≥ 1), dont la transcendance est une conséquence de celle de π, peu de résultats sont actuellement connus sur la natureExpand
Hypergeometric functions and irrationality measures
• in: Analytic Number Theory (Kyoto,
• 1996
On irrationality measures of the values of Gauss hypergeometric function
• Mathematics
• 1993
The paper gives irrationality measures for the values of some Gauss hypergeometric functions both in the archimedean andp-adic case. Further, an improvement of general results is obtained in the caseExpand