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COMPUTING L-FUNCTIONS AND SEMISTABLE REDUCTION OF SUPERELLIPTIC CURVES

Part of: Arithmetic algebraic geometry Arithmetic problems. Diophantine geometry

Published online by Cambridge University Press:  10 June 2016

IRENE I. BOUW  and
STEFAN WEWERS
IRENE I. BOUW
Affiliation:
Institut für Reine Mathematik, Universität Ulm, Helmholtzstr. 18, 89081 Ulm e-mails: irene.bouw@uni-ulm.de, stefan.wewers@uni-ulm.de
STEFAN WEWERS
Affiliation:
Institut für Reine Mathematik, Universität Ulm, Helmholtzstr. 18, 89081 Ulm e-mails: irene.bouw@uni-ulm.de, stefan.wewers@uni-ulm.de
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Abstract

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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.

MSC classification

Primary: 11G40: $L$-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture
Secondary: 14G10: Zeta-functions and related questions (Birch-Swinnerton-Dyer conjecture) 11G20: Curves over finite and local fields

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 59 , Issue 1 , January 2017 , pp. 77 - 108
Copyright
Copyright © Glasgow Mathematical Journal Trust 2016 

References

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