Geodesic
Reprint: On the approximation of logarithms of algebraic numbers (1953)
Documenta mathematica, Mahler Selecta (2019), pp. 527-555.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Mahler gives a new identity by means of which infinitely many algebraic functions approximating the logarithmic function are obtained. On substituting numerical algebraic values for the variable, a lower bound for the distance of its logarithm from variable algebraic numbers is found. As a further application, Mahler proves that the fractional part of the number $e^a$ is greater than $a^{-40a}$ for every sufficiently large positive integer $a$. \par Reprint of the author's paper [Philos. Trans. R. Soc. Lond., Ser. A 245, 371--398 (1953; Zbl 0052.04404)].
Classification : 11-03, 11J68 
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     author = {Mahler, Kurt},
     title = {Reprint: {On} the approximation of logarithms of algebraic numbers (1953)},
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Mahler, Kurt. Reprint: On the approximation of logarithms of algebraic numbers (1953). Documenta mathematica, Mahler Selecta (2019), pp. 527-555. http://geodesic.mathdoc.fr/item/DOCMA_2019__S1__a29/