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COMPUTING L-FUNCTIONS AND SEMISTABLE REDUCTION OF SUPERELLIPTIC CURVES

Published online by Cambridge University Press:  10 June 2016

IRENE I. BOUW
Affiliation:
Institut für Reine Mathematik, Universität Ulm, Helmholtzstr. 18, 89081 Ulm e-mails: [email protected], [email protected]
STEFAN WEWERS
Affiliation:
Institut für Reine Mathematik, Universität Ulm, Helmholtzstr. 18, 89081 Ulm e-mails: [email protected], [email protected]
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Abstract

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We give an explicit description of the stable reduction of superelliptic curves of the form yn=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.

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 2016 

References

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