English

On Mahler's transcendence measure for $e$

Number Theory 2018-05-03 v3

Abstract

We present a completely explicit transcendence measure for ee. 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 ee. 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}
}

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