Quantum computation of zeta functions of curves
Number Theory
2007-05-23 v3
Abstract
We exhibit a quantum algorithm for determining the zeta function of a genus g curve over a finite field 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.
Keywords
Cite
@article{arxiv.math/0411623,
title = {Quantum computation of zeta functions of curves},
author = {Kiran S. Kedlaya},
journal= {arXiv preprint arXiv:math/0411623},
year = {2007}
}
Comments
17 pages; v3 (refereed version): minor corrections