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Quantum computation of zeta functions of curves

Research paper by Kiran S. Kedlaya

Indexed on: 29 Nov '05Published on: 29 Nov '05Published in: Mathematics - Number Theory



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.