Computation of $λ_{K/F}$-function, where $K/F$ is a finite Galois extension

Sazzad Ali Biswas

Published 2015-06-09Version 1

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