University of Oulu

Leppälä, K., Matala-aho, T., Törmä, T. (2017) Rational approximations of the exponential function at rational points. Journal of Number Theory, 179, 220-239. doi:10.1016/j.jnt.2017.03.014

Rational approximations of the exponential function at rational points

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Author: Leppälä, Kalle1; Matala-aho, Tapani2; Törmä, Topi2
Organizations: 1Bioinformatics Research Centre, Aarhus University
2Mathematics, University of Oulu
Format: article
Version: accepted version
Access: open
Online Access: PDF Full Text (PDF, 2.8 MB)
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Language: English
Published: Elsevier, 2017
Publish Date: 2019-05-17


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 \(|s| \ge 3\) we improve existing results by extracting a large common factor from the numerators and the denominators of the convergents of that generalized continued fraction.

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Series: Journal of number theory
ISSN: 0022-314X
ISSN-E: 1096-1658
ISSN-L: 0022-314X
Volume: 179
Pages: 220 - 239
DOI: 10.1016/j.jnt.2017.03.014
Type of Publication: A1 Journal article – refereed
Field of Science: 111 Mathematics
Funding: The work of Topi Törmä was supported by the Väisälä foundation.
Copyright information: © 2017 Elsevier Inc. All rights reserved. This manuscript version is made available under the CC-BY-NC-ND 4.0 license