Mahler measures in a field are dense modulo 1 |
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Authors: | Artūras Dubickas |
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Affiliation: | (1) Department of Mathematics and Informatics, Vilnius University, Naugarduko 24, Vilnius, LT-03225, Lithuania |
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Abstract: | Let K be a number field. We prove that the set of Mahler measures M(α), where α runs over every element of K, modulo 1 is everywhere dense in [0, 1], except when or , where D is a positive integer. In the proof, we use a certain sequence of shifted Pisot numbers (or complex Pisot numbers) in K and show that the corresponding sequence of their Mahler measures modulo 1 is uniformly distributed in [0, 1]. Received: 24 March 2006 |
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Keywords: | 11K06 11R06 |
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