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Reciprocal Algebraic Integers Whose Mahler Measures are Non-Reciprocal

Published online by Cambridge University Press:  20 November 2018

David W. Boyd
David W. Boyd*
Affiliation:
Department of Mathematics University of British Columbia Vancouver, B.C., Canada V6T 1Y4
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Abstract

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The Mahler measure M (α) of an algebraic integer α is the product of the moduli of the conjugates of α which lie outside the unit circle. A number α is reciprocal if α- 1 is a conjugate of α. We give two constructions of reciprocal a for which M (α) is non-reciprocal producing examples of any degree n of the form 2h with h odd and h ≥ 3, or else of the form with s ≥ 2. We give explicit examples of degrees 10, 14 and 20.

Keywords

Primary 12A10Secondary 12A55

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 30 , Issue 1 , 01 March 1987 , pp. 3 - 8
Copyright
Copyright © Canadian Mathematical Society 01

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