Reprint: On the approximation of logarithms of algebraic numbers (1953) (Q1996505)

Summary: 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 \(a\). Reprint of the author's paper [Philos. Trans. R. Soc. Lond., Ser. A 245, 371--398 (1953; Zbl 0052.04404)].