Epsilon factors of symplectic type characters in the wild case

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.