# On the irrationality measure of log3

@article{Wu2014OnTI,
title={On the irrationality measure of log3},
author={Qiang Wu and Lihong Wang},
journal={Journal of Number Theory},
year={2014},
volume={142},
pages={264-273}
}
• Published 2014
• Mathematics
• Journal of Number Theory
Abstract In this paper, we obtain a new estimate of an irrationality measure of the number log 3 . We have μ ( log 3 ) ≤ 5.1163051 with an “arithmetical method”. The previous results were μ ( log 3 ) ≤ 8.616 … by G. Rhin in 1987 and μ ( log 3 ) ≤ 5.125 … by V.H. Salikhov in 2007.
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A general theorem is given on the linear independence measure of logarithms of rational numbers and, in particular, the linearindependence measure of 1, log 2, log 3, log 5 and of 2, 3, 4 and 5. Expand
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Let Mp'a) be thepth root of the mean absolute values of the/?th powers of a totally real algebraic integer a. For each fixedp > 0 we study the set 911. of such Mp(a). We show that its structure is asExpand