On the heights of totally p-adic numbers

TL;DR

This paper uses potential theory to extend and refine bounds on the Weil height of totally p-adic numbers, improving previous results under certain integrality conditions.

Contribution

It generalizes existing upper bounds on Weil heights for totally p-adic numbers and offers slight improvements under integrality assumptions.

Findings

Extended upper bounds for Weil heights using potential theory

Improved bounds under integrality conditions

Generalized bounds for fields of totally p-adic numbers

Abstract

Bombieri and Zannier established lower and upper bounds for the limit infimum of the Weil height in fields of totally p-adic numbers and generalizations thereof. In this paper, we use potential theoretic techniques to generalize the upper bounds from their paper and, under the assumption of integrality, to improve slightly upon their bounds.