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arXiv · 1704.01374

On Mahler's transcendence measure for $e$

Anne-Maria Ernvall-Hytönen·Tapani Matala-aho·Louna Seppälä
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Abstract

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-Pad\'e approximations and on careful analysis of common factors in the footsteps of Hata.

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Anne-Maria Ernvall-Hytönen, Tapani Matala-aho, Louna Seppälä. 2017-04-05. On Mahler's transcendence measure for $e$. https://doi.org/10.1007/s00365-018-9429-3

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