Mahler measures in a field are dense modulo 1

Author: Dubickas Arturas  

Publisher: Springer Publishing Company

ISSN: 0003-889X

Source: Archiv der Mathematik, Vol.88, Iss.1, 2007-01, pp. : 29-34

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Abstract

Let K</i> be a number field. We prove that the set of Mahler measures M</i>(α), where α runs over every element of K</i>, modulo 1 is everywhere dense in [0, 1], except when </equationsource> or </equationsource> , where D</i> is a positive integer. In the proof, we use a certain sequence of shifted Pisot numbers (or complex Pisot numbers) in K</i> and show that the corresponding sequence of their Mahler measures modulo 1 is uniformly distributed in [0, 1].