Rational approximations of the exponential function at rational points
- Resource Type
- Working Paper
- Authors
- Leppälä, Kalle; Matala-aho, Tapani; Törmä, Topi
- Source
- Subject
- Mathematics - Number Theory
11J82 (primary), 11J70, 11A55 (secondary)
- Language
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.