Approximate computations with modular curves

被引：0

作者：

Couveignes, Jean-Marc ^{[1
]}

Edixhoven, Bas ^{[2
]}

机构：

[1] Univ Bordeaux, IMB CNRS INRIA, UMR 5251, F-33400 Talence, France

[2] Leiden Univ, Math Inst, NL-2333 CA Leiden, Netherlands

来源：

GEOMETRY AND ARITHMETIC | 2012年

关键词：

Galois representations; modular curves; Ramanujan tau-function; inverse Jacobi problem; FORMULAS; SUMS;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This article gives an introduction for mathematicians interested in numerical computations in algebraic geometry and number theory to some recent progress in algorithmic number theory, emphasising the key role of approximate computations with modular curves and their Jacobians. These approximations are done in polynomial time in the dimension and the required number of significant digits. We explain the main ideas of how the approximations are done, illustrating them with examples, and we sketch some applications in number theory.

引用

页码：91 / +

页数：4