Experimental Mathematics

New Methods Providing High Degree Polynomials with Small Mahler Measure

G. Rhin and J.-M. Sac-Épée

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Abstract

In this work, we propose two new methods devoted to provide a large list of new polynomials with high degree and small Mahler measure. First, by statistical considerations, we augment Mossinghoff's list of polynomials with degree at most 180, and then we give a new list of such polynomials of degree up to 300. The second idea is to perturb polynomials of Mossinghoff's list, and for higher degrees, of this new list, and to use them as initial polynomials for a minimization method, which converges to new polynomials with lower Mahler measure.

Article information

Source
Experiment. Math., Volume 12, Number 4 (2003), 457-462.

Dates
First available in Project Euclid: 18 June 2004

Permanent link to this document
https://projecteuclid.org/euclid.em/1087568021

Mathematical Reviews number (MathSciNet)
MR2043995

Zentralblatt MATH identifier
1075.11065

Subjects
Primary: 12\_04 11Y40: Algebraic number theory computations

Keywords
Mahler measure polynomials table random drawings

Citation

Rhin, G.; Sac-Épée, J.-M. New Methods Providing High Degree Polynomials with Small Mahler Measure. Experiment. Math. 12 (2003), no. 4, 457--462. https://projecteuclid.org/euclid.em/1087568021


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