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

  • Kurt Mahler


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 eae^a is greater than a40aa^{-40a} for every sufficiently large positive integer aa.

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