# Epsilon factors of symplectic type characters in the wild case

## TL;DR

This paper explicitly determines the signs of epsilon factors for symplectic characters of local fields in the wild ramification case, extending Tate's work to more complex extensions.

## Contribution

It provides explicit formulas for epsilon factor signs for symplectic characters in wildly ramified quadratic extensions, a case not previously fully understood.

## Key findings

- Explicit signs of epsilon factors determined for symplectic characters
- Results apply to wildly ramified quadratic extensions
- Extends Tate's framework to complex ramification scenarios

## Abstract

By work of John Tate we can associate an epsilon factor with every multiplicative character of a local field. In this paper we determine the explicit signs of the epsilon factors for symplectic type characters of $K^\times$, where $K/F$ is a wildly ramified quadratic extension of a non-Archimedean local field $F$ of characteristic zero.