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The irrationality of
Authors:Masayoshi Hata
Affiliation:Division of Mathematics, Faculty of Integrated Human Studies, Kyoto University, Kyoto 606-01, Japan
Abstract:We shall show that the numbers $1, log (1+ 1/q), log (1-1/q)$ and
$log (1+1/q)log (1-1/q)$ are linearly independent over $mathbf{Q}$ for any natural number $q ge 54$. The key is to construct explicit Padé-type approximations using Legendre-type polynomials.

Keywords:Logarithm   linear independence measure   Pad'{e} approximation
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