Zeros of the Alexander polynomial of knot

Abstract

The leading coefficient of the Alexander polynomial of a knot is the most informative element derived from this invariant, and the growth of orders of the first homology of cyclic branched covering spaces is also a familiar subject. Accordingly, there are a lot of investigations in each subject. However, there is no study which deals with both subjects in the same context. In this paper, we show that the two subjects are closely related in $p$-adic number theory and dynamical systems.