Rational approximations of the exponential function at rational points
Leppälä, Kalle; Matala-aho, Tapani; Törmä, Topi (2017-05-18)
Leppälä, Kalle
Matala-aho, Tapani
Törmä, Topi
Elsevier
18.05.2017
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
https://creativecommons.org/licenses/by-nc-nd/4.0/
© 2017 Elsevier Inc. All rights reserved. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
https://creativecommons.org/licenses/by-nc-nd/4.0/
© 2017 Elsevier Inc. All rights reserved. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
https://creativecommons.org/licenses/by-nc-nd/4.0/
Julkaisun pysyvä osoite on
https://urn.fi/URN:NBN:fi-fe201901172348
https://urn.fi/URN:NBN:fi-fe201901172348
Tiivistelmä
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 \(|s| \ge 3\) we improve existing results by extracting a large common factor from the numerators and the denominators of the convergents of that generalized continued fraction.
Kokoelmat
- Avoin saatavuus [31941]