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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) |
| Persistent link: | http://urn.fi/urn:nbn:fi-fe201901172348 |
| Language: | English |
| Published: |
Elsevier,
2017
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| Publish Date: | 2019-05-17 |
| Description: |
AbstractWe 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. see all
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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 |
| OADOI: | https://oadoi.org/10.1016/j.jnt.2017.03.014 |
| Type of Publication: |
A1 Journal article – refereed |
| Field of Science: |
111 Mathematics |
| Subjects: | |
| 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 http://creativecommons.org/licenses/by-nc-nd/4.0/ |
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https://creativecommons.org/licenses/by-nc-nd/4.0/ |