arXiv subjects

Akio Noguchi

Publications and source records attributed to Akio Noguchi.

2 recordsLinked to original sources

arXiv2005

Zeros of the Alexander polynomial of knot

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.

math.GT↗

arXiv2005

A functional equation for the Lefschetz zeta functions of infinite cyclic coverings with an application to knot theory

The Weil conjecture is a delightful theorem for algebraic varieties on finite fields and an important model for dynamical zeta functions. In this paper, we prove a functional equation of Lefschetz zeta functions for infinite cyclic coverings which is analogous to the Weil conjecture. Applying this functional equation to knot theory, we obtain a new view point on the reciprocity of the Alexander polynomial of a knot.

math.GT↗