English

Rational approximations of the exponential function at rational points

Number Theory 2016-09-23 v1

Abstract

We give explicit and asymptotic lower bounds for the quantity es/tM/N|e^{s/t}-M/N| by studying a generalized continued fraction expansion of es/te^{s/t}. In cases s3|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.

Keywords

Cite

@article{arxiv.1609.07076,
  title  = {Rational approximations of the exponential function at rational points},
  author = {Kalle Leppälä and Tapani Matala-aho and Topi Törmä},
  journal= {arXiv preprint arXiv:1609.07076},
  year   = {2016}
}
R2 v1 2026-06-22T15:58:15.476Z