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THE MAHLER MEASURE OF POLYNOMIALS WITH ODD COEFFICIENTS

Published online by Cambridge University Press:  28 April 2004

PETER BORWEIN ,
KEVIN G. HARE  and
MICHAEL J. MOSSINGHOFF
PETER BORWEIN
Affiliation:
Department of Mathematics and Statistics, Simon Fraser University, Burnaby, B.C. V5A 1S6, Canadapborwein@cecm.sfu.ca
KEVIN G. HARE
Affiliation:
Department of Mathematics, University of California, Berkeley, CA 94720, USAkghare@math.berkeley.edu
MICHAEL J. MOSSINGHOFF
Affiliation:
Department of Mathematics, Davidson College, Davidson, NC 28035, USAmjm@member.ams.org
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Abstract

The minimum value of the Mahler measure of a nonreciprocal polynomial whose coefficients are all odd integers is proved here to be the golden ratio. The smallest measures of reciprocal polynomials with $\pm1$ coefficients and degree at most 72 are also determined.

Keywords

11R09 (primary)11C0811Y40 (secondary)
Type
Papers
Information
Bulletin of the London Mathematical Society , Volume 36 , Issue 3 , May 2004 , pp. 332 - 338
Copyright
© The London Mathematical Society 2004

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