# Quantum computation of zeta functions of curves

@article{Kedlaya2006QuantumCO, title={Quantum computation of zeta functions of curves}, author={Kiran S. Kedlaya}, journal={computational complexity}, year={2006}, volume={15}, pages={1-19} }

Abstract.We exhibit a quantum algorithm for determining the zeta function of a genus g curve over a finite field
$$ \mathbb{F}_{q} $$, which is polynomial in g and log(q). This amounts to giving an algorithm to produce provably random elements of the class group of a curve, plus a recipe for recovering a Weil polynomial from enough of its cyclic resultants. The latter effectivizes a result of Fried in a restricted setting.

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