  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.
