Lehmer’s problem for compact Abelian groups

Lind, Douglas

doi:10.1090/S0002-9939-04-07753-6

Lehmer’s problem for compact Abelian groups
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by Douglas Lind

Proc. Amer. Math. Soc. 133 (2005), 1411-1416

DOI: https://doi.org/10.1090/S0002-9939-04-07753-6

Published electronically: October 18, 2004

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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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