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2005 Small Limit Points of Mahler's Measure
David W. Boyd, Michael J. Mossinghoff
Experiment. Math. 14(4): 403-414 (2005).

Abstract

Let $M(P(z_1,\dots,z_n))$ denote Mahler's measure of the polynomial $P(z_1,\dots,z_n)$. Measures of polynomials in $n$ variables arise naturally as limiting values of measures of polynomials in fewer variables. We describe several methods for searching for polynomials in two variables with integer coefficients having small measure, demonstrate effective methods for computing these measures, and identify 48 polynomials $P(x,y)$ with integer coefficients, irreducible over $\Rats$, for which $1 < M(P(x,y)) < 1.37$.

Citation

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David W. Boyd. Michael J. Mossinghoff. "Small Limit Points of Mahler's Measure." Experiment. Math. 14 (4) 403 - 414, 2005.

Information

Published: 2005
First available in Project Euclid: 10 January 2006

zbMATH: 1152.11343
MathSciNet: MR2193803

Subjects:
Primary: 11C08
Secondary: 11R09 , 11Y35

Keywords: Lehmer's problem , Mahler measure

Rights: Copyright © 2005 A K Peters, Ltd.

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