On Mahler's transcendence measure for $e$
Number Theory
2018-05-03 v3
Abstract
We present a completely explicit transcendence measure for . 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 . The results are based on Hermite-Pad\'e approximations and on careful analysis of common factors in the footsteps of Hata.
Cite
@article{arxiv.1704.01374,
title = {On Mahler's transcendence measure for $e$},
author = {Anne-Maria Ernvall-Hytönen and Tapani Matala-aho and Louna Seppälä},
journal= {arXiv preprint arXiv:1704.01374},
year = {2018}
}
Comments
1 figure