Quantum computation of zeta functions of curves

被引：12

作者：

Kedlaya, KS ^{[1
]}

机构：

[1] MIT, Dept Math, Cambridge, MA 02139 USA

来源：

COMPUTATIONAL COMPLEXITY | 2006年 / 15卷 / 01期

基金：

美国国家科学基金会;

关键词：

quantum computation; zeta functions; class groups; algebraic curves; finite fields; cyclic resultants;

D O I：

10.1007/s00037-006-0204-7

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We exhibit a quantum algorithm for determining the zeta function of a genus g curve over a finite field Fq, 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.

引用

页码：1 / 19

页数：19

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