On Roots of Polynomials with Positive Coefficients
Bombieri and Zannier established lower and upper bounds for the limit infimum of the Weil height in fields of totally -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.
We consider the sequence of fractional parts , , where is a Pisot number and 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 and the unique limit point is zero, was earlier described by the author and Luca, independently.