紧阿贝尔群的Lehmer问题
Lehmer's Problem for compact abelian groups
摘要：
本文对一般紧阿贝尔群，提出了多项式的Mahler测度的Lehmer问题，并对每个紧阿贝尔群引入了一个Lehmer常数.证明了所有非平凡连通紧群具有相同的Lehmer常数，并对有限循环群的Lehmer常数值进行了猜想.我们还表明，如果一个组有无穷多个连通组件，然后它的Lehmer常数为零。
英文摘要：
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.
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