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On the heights of totally p -adic numbers

Paul Fili (2014)

Journal de Théorie des Nombres de Bordeaux

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.

On the limit points of the fractional parts of powers of Pisot numbers

Artūras Dubickas (2006)

Archivum Mathematicum

We consider the sequence of fractional parts { ξ α n } , n = 1 , 2 , 3 , , where α > 1 is a Pisot number and ξ ( α ) is a positive number. We find the set of limit points of this sequence and describe all cases when it has a unique limit point. The case, where ξ = 1 and the unique limit point is zero, was earlier described by the author and Luca, independently.

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