arXiv:1402.6758 Abstract | arXiv Analytics

arXiv:1402.6758 [math.NT]Abstract References Reviews Resources

Counting points on curves using a map to P^1

Published 2014-02-27, updated 2014-09-10Version 2

We introduce a new algorithm to compute the zeta function of a curve over a finite field. This method extends Kedlaya's algorithm to a very general class of curves using a map to the projective line. We develop all the necessary bounds, analyse the complexity of the algorithm and provide some examples computed with our implementation.

Categories: math.NT, math.AG

Keywords: counting points, method extends kedlayas algorithm, finite field, necessary bounds, zeta function

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