Rational approximations of the exponential function at rational points

Kalle Leppälä, Tapani Matala-aho, Topi Törmä

Published 2016-09-22Version 1

We give explicit and asymptotic lower bounds for the quantity $|e^{s/t}-M/N|$ by studying a generalized continued fraction expansion of $e^{s/t}$. In cases $|s|\geq 3$ we improve existing results by extracting a large common factor from the numerators and the denominators of the convergents of that generalized continued fraction.