Lehmer's Problem for compact abelian groups
数论
2015-12-23 v2 动力系统
摘要
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.
引用
@article{arxiv.math/0303279,
title = {Lehmer's Problem for compact abelian groups},
author = {Douglas Lind},
journal= {arXiv preprint arXiv:math/0303279},
year = {2015}
}
备注
7 pages, minor revision, accepted for Proc. Amer. Math. Soc