On the heights of totally p-adic numbers
Journal de Théorie des Nombres de Bordeaux, Volume 26 (2014) no. 1, pp. 103-109.

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.

Bombieri et Zannier ont démontré des minorations et des majorations de la limite inférieure de la hauteur de Weil sur le corps des nombres totalement p-adiques et sur leurs généralisations. Dans notre étude nous utilisons des techniques de la théorie du potentiel pour généraliser les majorations de leur étude et, dans l’hypothèse d’intégralité, améliorer un peu plus les minorations.

Received:
Accepted:
Published online:
DOI: 10.5802/jtnb.861
Classification: 11G50,  11R06,  37P30
Keywords: Weil height, totally p-adic, potential theory, Fekete-Szegő theorem.
Paul Fili 1

1 Department of Mathematics University of Rochester, Rochester, NY 14627
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Paul Fili. On the heights of totally $p$-adic numbers. Journal de Théorie des Nombres de Bordeaux, Volume 26 (2014) no. 1, pp. 103-109. doi : 10.5802/jtnb.861. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.861/

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