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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Lehmer's problem for compact Abelian groups


Author: Douglas Lind
Journal: Proc. Amer. Math. Soc. 133 (2005), 1411-1416
MSC (2000): Primary 43A40, 22D40; Secondary 37B40, 11G50
Published electronically: October 18, 2004
MathSciNet review: 2111966
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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
Email: lind@math.washington.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07753-6
PII: S 0002-9939(04)07753-6
Keywords: Lehmer's Problem, Mahler measure, compact abelian group
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
Article copyright: © Copyright 2004 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.