Computing $L$-functions and semistable reduction of superelliptic curves

Abstract

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

major revision, 34 pages

References in corpus (1)

• Another proof of the Semistable Reduction Theorem

Cited by in corpus (4)

• A database of genus 2 curves over the rational numbers
• Conductor and discriminant of Picard curves
• Modular invariants for genus 3 hyperelliptic curves
• Zeta Functions on Arithmetic Surfaces