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We give an extension of Fox's formula of the Alexander polynomial for doublebranched covers over the three-sphere. Our formula provides the Reidemeistertorsion of a double branched cover along a knot for a non-trivial onedimensional representation by the product of two factors derived from the knotgroup. One of the factors is determined by the twisted Alexander polynomial andthe other is determined by a rational function on the character variety. As anapplication, we show that these products distinguish isotopy classes oftwo-bridge knots up to mirror images.

Twisted Alexander polynomials, character varieties and Reidemeister torsion of double branched covers