A p-adic analog of Hasse-Davenport product relation involving epsilon-factors

Abstract

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.