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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Lehmer’s problem for compact Abelian groups
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by Douglas Lind PDF
Proc. Amer. Math. Soc. 133 (2005), 1411-1416 Request permission

Abstract:

We formulate Lehmer’s Problem concerning the Mahler measure of polynomials for general compact abelian groups, introducing a Lehmer constant for each such group. We show that all nontrivial connected compact groups have the same Lehmer constant and conjecture the value of the Lehmer constant for finite cyclic groups. We also show that if a group has infinitely many connected components, then its Lehmer constant vanishes.
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Additional Information
  • Douglas Lind
  • Affiliation: Department of Mathematics, Box 354350, University of Washington, Seattle, Washington 98195–4350
  • MR Author ID: 114205
  • Email: lind@math.washington.edu
  • Received by editor(s): September 12, 2003
  • Received by editor(s) in revised form: January 7, 2004
  • Published electronically: October 18, 2004
  • Communicated by: Wen-Ching Winnie Li
  • © Copyright 2004 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 133 (2005), 1411-1416
  • MSC (2000): Primary 43A40, 22D40; Secondary 37B40, 11G50
  • DOI: https://doi.org/10.1090/S0002-9939-04-07753-6
  • MathSciNet review: 2111966