  In this paper we prove some generalizations of the classical Hasse-Davenport
product relation for certain arithmetic factors defined on p-adic fields, among
them one finds the epsilon-factors appearing in Tate's thesis. We then show
that these generalizations are equivalent to some representation theoretic
identities relating the determinant of ramified local coefficients matrices
defined for coverings of SL(2,F) to Plancherel measures and gamma-factors.
