A $p$-adic lower bound for a linear form in logarithms

Neea Palojärvi; Louna Seppälä

A $p$-adic lower bound for a linear form in logarithms

Number Theory 2022-05-19 v2

Authors: Neea Palojärvi , Louna Seppälä

Abstract

Linear forms in logarithms have an important role in the theory of Diophantine equations. In this article, we prove explicit $p$ -adic lower bounds for linear forms in $p$ -adic logarithms of rational numbers using Pad\'e approximations of the second kind.

Keywords

p-adic analysis p-adic hodge theory upper bounds

Cite

@article{arxiv.2107.00971,
  title  = {A $p$-adic lower bound for a linear form in logarithms},
  author = {Neea Palojärvi and Louna Seppälä},
  journal= {arXiv preprint arXiv:2107.00971},
  year   = {2022}
}

Comments

27 pages

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