Approximate computations with modular curves
Number Theory
2012-05-29 v1 Algebraic Geometry
Abstract
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.
Cite
@article{arxiv.1205.5896,
title = {Approximate computations with modular curves},
author = {Jean-Marc Couveignes and Bas Edixhoven},
journal= {arXiv preprint arXiv:1205.5896},
year = {2012}
}