Evaluating Igusa functions
Number Theory
2011-01-24 v2
Abstract
The moduli space of principally polarized abelian surfaces is parametrized by three Igusa functions. In this article we investigate a new way to evaluate these functions by using Siegel Eisenstein series. We explain how to compute the Fourier coefficients of certain Siegel modular forms using classical modular forms of half-integral weight. One of the results in this paper is an explicit algorithm to evaluate the Igusa functions to a prescribed precision.
Cite
@article{arxiv.1005.1234,
title = {Evaluating Igusa functions},
author = {Reinier Broker and Kristin Lauter},
journal= {arXiv preprint arXiv:1005.1234},
year = {2011}
}