Abstract

In this paper we consider the set of Mahler measures of generalized Pisot and Salem numbers and give a characterization of such numbers in terms of their minimal polynomials. We show that every real quadratic algebraic integer β can be expressed by the difference of the Mahler measure of a generalized Pisot number and a Pisot number in ℚ(β).

中文翻译：

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皮索和塞勒姆类型数的马勒测量

摘要

在本文中，我们考虑广义 Pisot 和 Salem 数的一组 Mahler 测度，并根据它们的最小多项式给出这些数的表征。我们证明了每个实数二次代数整数β都可以通过广义皮索数的马勒测度与 ℚ( β ) 中的皮索数的差来表示。