Computing L-functions of $\hat{I}»$-adic representations of global function fields

Abstract

The L-function $L(\ddot{I}{}_{\hat{I}}»,s)$ of an almost everywhere unramified $\hat{I}»$-adic representation $\ddot{I}{}_{\hat{I}}»$ of a global function field ${\mathbb{F}}_q(C)$ is known to be a rational function in $q^{-s}$ satisfying a functional equation up to some complex sign $\hat{I}\mu (\ddot{I}{}_{\hat{I}}»)$. This paper presents a systematic framework to compute the coefficients of $L(\ddot{I}{}_{\hat{I}}»,s)$ and its sign $\hat{I}\mu (\ddot{I}{}_{\hat{I}}»)$ with some explicit examples.

19 pages