Computation of the Lambda function for a finite Galois extension

Abstract

By Langlands and Deligne we know that the local constants are extendible functions. Therefore, to give an explicit formula of the local constant of an induced representation of a local Galois group of a non-Archimedean local field $F$ of characteristic zero, we have to compute the lambda function $\lambda_{K/F}$ for a finite extension $K/F$. In this paper, when a finite extension $K/F$ is Galois, we give a formula for $\lambda_{K/F}$.