A short proof for the relation between Weil indices and 𝜖-factors

Abstract

ABSTRACTLet F be a finite extension of ℚp and let ψ be a non-trivial character of F. For a∈F* let γ(a,ψ) be the normalized Weil index splitting the Hilbert symbol. In this short note we give a simple proof for the relation where ηa is the quadratic character of F* whose kernel is and where 𝜖(⋅,⋅,⋅) is the epsilon factor appearing in Tate’s thesis.