COMPUTING<i>L</i>-FUNCTIONS AND SEMISTABLE REDUCTION OF SUPERELLIPTIC CURVES

Abstract

Abstract We give an explicit description of the stable reduction of superelliptic curves of the form y n = f ( x ) at primes $\mathfrak{p}$ whose residue characteristic is prime to the exponent n . We then use this description to compute the local L -factor and the exponent of conductor at $\mathfrak{p}$ of the curve.