Computation of the Lambda function for a finite Galois extension

TL;DR

This paper derives an explicit formula for the lambda function associated with a finite Galois extension of local fields, which is essential for understanding local constants in number theory.

Contribution

It provides a new explicit formula for the lambda function in the case of Galois extensions, advancing the computation of local constants in number theory.

Findings

Explicit formula for lambda function for Galois extensions

Improved understanding of local constants in number theory

Extension of Langlands and Deligne's work

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 $\lambda_{K/F}$.