Lehmer's Problem for compact abelian groups

Details Lehmer's Problem for compact abelian groups Lehmer's Problem for compact abelian groups

2003-03-23

arxiv.org/abs/math/0303279v2

Mathematics

Number Theory

7 pages, minor revision, accepted for Proc. Amer. Math. Soc

Scientific paper

We formulate Lehmer's Problem about 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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