Evaluating Igusa functions

Details Evaluating Igusa functions Evaluating Igusa functions

2010-05-07

arxiv.org/abs/1005.1234v2

Mathematics

Number Theory

Scientific paper

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.

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