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

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

2005-05-25

arxiv.org/abs/math/0505531v1

Mathematics

Geometric Topology

11 pages

Scientific paper

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.

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