Counting points on curves using a map to P¹
classification
🧮 math.NT
math.AG
keywords
algorithmcurvesanalyseboundsclasscomplexitycomputecomputed
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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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