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On Mahler’s transcendence measure for e |
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| Author: | Ernvall-Hytönen, Anne-Maria1; Matala-aho, Tapani2; Seppälä, Louna2 |
| Organizations: |
1Matematik och Statistik, Åbo Akademi University, Domkyrkotorget 1, 20500, Åbo, Finland 2Matematiikka, Oulun yliopisto, PL 8000, 90014, Oulu, Finland |
| Format: | article |
| Version: | accepted version |
| Access: | open |
| Online Access: | PDF Full Text (PDF, 0.4 MB) |
| Persistent link: | http://urn.fi/urn:nbn:fi-fe202003097690 |
| Language: | English |
| Published: |
Springer Nature,
2019
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| Publish Date: | 2020-03-09 |
| Description: |
AbstractWe present a completely explicit transcendence measure for e. This is a continuation and an improvement to the works of Borel, Mahler, and Hata on the topic. Furthermore, we also prove a transcendence measure for an arbitrary positive integer power of e. The results are based on Hermite–Padé approximations and on careful analysis of common factors in the footsteps of Hata. see all
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| Series: |
Constructive approximation |
| ISSN: | 0176-4276 |
| ISSN-E: | 1432-0940 |
| ISSN-L: | 0176-4276 |
| Volume: | 49 |
| Issue: | 2 |
| Pages: | 405 - 444 |
| DOI: | 10.1007/s00365-018-9429-3 |
| OADOI: | https://oadoi.org/10.1007/s00365-018-9429-3 |
| Type of Publication: |
A1 Journal article – refereed |
| Field of Science: |
111 Mathematics |
| Subjects: | |
| Funding: |
The work of the author Louna Seppälä was supported by the Magnus Ehrnrooth Foundation. The work of the author Anne-Maria Ernvall-Hytönen was supported by the Academy of Finland Project 303820 and by the Finnish Cultural Foundation. |
| Copyright information: |
© Springer Science+Business Media, LLC, part of Springer Nature 2018. his is a post-peer-review, pre-copyedit version of an article published in Constr Approx. The final authenticated version is available online at https://doi.org/10.1007/s00365-018-9429-3.
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