Twisting Alexander Invariants with Periodic Representations

Twisted Alexander invariants have been defined for any knot and linear representation of its group. The invariants are generalized for any periodic representation of the commutator subgroup of the knot group. Properties of the new twisted invariants are given. Under suitable hypotheses, reciprocality and bounds on the moduli of zeros are obtained. A topological interpretation of the Mahler measure of the invariants is presented. Keywords: Knot, twisted Alexander polynomial, representation shift, Mahler measure.