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 | References | Similar Articles | Additional Information

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

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.