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THE MAHLER MEASURE OF TRINOMIALS OF HEIGHT 1

Published online by Cambridge University Press:  01 April 2014

V. FLAMMANG
V. FLAMMANG*
Affiliation:
UMR CNRS 7502, IECL, Université de Lorraine, Département de Mathématiques, UFR MIM, Ile du Saulcy, 57045 Metz cedex 01, France email valerie.flammang@univ-lorraine.fr
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Abstract

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We study the Mahler measure of the trinomials ${z}^{n} \pm {z}^{k} \pm 1$. We give two criteria to identify those whose Mahler measure is less than $1. 381\hspace{0.167em} 356\cdots = M(1+ {z}_{1} + {z}_{2} )$. We prove that these criteria are true for $n$ sufficiently large.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 96 , Issue 2 , April 2014 , pp. 231 - 243
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

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