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

Akio Noguchi
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Abstract

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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Akio Noguchi. 2005-05-25. A functional equation for the Lefschetz zeta functions of infinite cyclic coverings with an application to knot theory. https://arxiv.org/abs/math/0505531

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