2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/100957We 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.17 pages; v3 (refereed version): minor correctionsNumber Theory11M38text