University of Oulu

Ernvall-Hytönen, A., Matala-aho, T. & Seppälä, L. On Mahler’s Transcendence Measure for e. Constr Approx 49, 405–444 (2019).

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)
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Language: English
Published: Springer Nature, 2019
Publish Date: 2020-03-09


We 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.

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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
Type of Publication: A1 Journal article – refereed
Field of Science: 111 Mathematics
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