ABSTRACT
We compute the L-functions of a large class of algebraic curves and verify the expected functional equation numerically. Our computations are based on our previous results on stable reduction to calculate the local L-factor and the conductor exponent at the primes of bad reduction. We mainly restrict to the case of hyperelliptic curves of genus g ⩾ 2 defined over that have semistable reduction at every prime p. We also discuss a few more general cases to illustrate the usefulness of our method for general superelliptic curves.
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2000 AMS SUBJECT CLASSIFICATION:
Acknowledgments
We thank the referees for very useful comments and suggestions. We are grateful to one of the referees for pointing out the reference [CitationLiu 96] to us, which contains many of the arguments from Section 3 to describe models of hyperelliptic curves in a similar form.