Counting points on curves using a map to 𝐏¹

Tuitman, Jan

doi:10.1090/mcom/2996

Counting points on curves using a map to $\mathbf {P}^1$
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Math. Comp. 85 (2016), 961-981 Request permission

Abstract:

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.

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