Twisting formula of epsilon factors

TL;DR

This paper derives a generalized twisting formula for epsilon factors of characters over non-Archimedean local fields using local Jacobi sums, extending existing explicit formulas.

Contribution

It introduces a new generalized twisting formula for epsilon factors, connecting them with local Jacobi sums, which was not previously available.

Findings

Provides explicit twisting formula for epsilon factors.

Links epsilon factors with local Jacobi sums.

Extends the theory of epsilon factors to more general cases.

Abstract

For characters of a non-Archimedean local field we have explicit formula for epsilon factors. But in general, we do not have any generalized twisting formula of epsilon factors. In this paper we give a generalized twisting formula of epsilon factors via local Jacobi sums.