Experimental Mathematics

Small Limit Points of Mahler's Measure

David W. Boyd and Michael J. Mossinghoff

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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 $1 < M(P(x,y)) < 1.37$.

Article information

Source
Experiment. Math., Volume 14, Issue 4 (2005), 403-414.

Dates
First available in Project Euclid: 10 January 2006

Permanent link to this document
https://projecteuclid.org/euclid.em/1136926971

Mathematical Reviews number (MathSciNet)
MR2193803

Zentralblatt MATH identifier
1152.11343

Subjects
Primary: 11C08: Polynomials [See also 13F20]
Secondary: 11R09: Polynomials (irreducibility, etc.) 11Y35: Analytic computations

Keywords
Lehmer's problem Mahler measure

Citation

Boyd, David W.; Mossinghoff, Michael J. Small Limit Points of Mahler's Measure. Experiment. Math. 14 (2005), no. 4, 403--414. https://projecteuclid.org/euclid.em/1136926971


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