  The leading coefficient of the Alexander polynomial of a knot is the most
informative element in 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 into each subject. However,
there is no study which deal with the both subjects in a same context. In this
paper, we show that the two subjects are closely related in p-adic number
theory and dynamical systems.
