Rational approximations of the exponential function at rational points
Year: 2016
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Institutions: Aarhus University, University of Oulu
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2950906181