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.
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页码：1 / 19
页数：19
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