### On the heights of totally $p$-adic numbers

Paul Fili (2014)

Journal de Théorie des Nombres de Bordeaux

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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.