  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.
