Quantum computation of zeta functions of curves

@article{Kedlaya2006QuantumCO,
  title={Quantum computation of zeta functions of curves},
  author={K. Kedlaya},
  journal={computational complexity},
  year={2006},
  volume={15},
  pages={1-19}
}
  • K. Kedlaya
  • Published 2006
  • Mathematics, Computer Science
  • computational complexity
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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