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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Polynomials with small Mahler measure
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by Michael J. Mossinghoff PDF
Math. Comp. 67 (1998), 1697-1705 Request permission

Abstract:

We describe several searches for polynomials with integer coefficients and small Mahler measure. We describe the algorithm used to test Mahler measures. We determine all polynomials with degree at most 24 and Mahler measure less than $1.3$, test all reciprocal and antireciprocal polynomials with height 1 and degree at most 40, and check certain sparse polynomials with height 1 and degree as large as 181. We find a new limit point of Mahler measures near $1.309$, four new Salem numbers less than $1.3$, and many new polynomials with small Mahler measure. None has measure smaller than that of Lehmer’s degree 10 polynomial.
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Additional Information
  • Michael J. Mossinghoff
  • Affiliation: Department of Mathematical Sciences, Appalachian State University, Boone, North Carolina 28608
  • MR Author ID: 630072
  • ORCID: 0000-0002-7983-5427
  • Email: mjm@math.appstate.edu
  • Received by editor(s): May 20, 1997
  • © Copyright 1998 American Mathematical Society
  • Journal: Math. Comp. 67 (1998), 1697-1705
  • MSC (1991): Primary 12--04; Secondary 11Y40
  • DOI: https://doi.org/10.1090/S0025-5718-98-01006-0
  • MathSciNet review: 1604391