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Mathematics of Computation

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Evaluating Igusa functions

Authors: Reinier Bröker and Kristin Lauter
Journal: Math. Comp. 83 (2014), 2977-2999
MSC (2010): Primary 11F46; Secondary 14J15
Published electronically: February 27, 2014
MathSciNet review: 3246819
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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 the 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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Additional Information

Reinier Bröker
Affiliation: Brown University, Box 1917, 151 Thayer Street, Providence, Rhode Island 02912

Kristin Lauter
Affiliation: Microsoft Research, One Microsoft Way, Redmond, Washington 98052

Received by editor(s): December 12, 2008
Received by editor(s) in revised form: June 28, 2012, and March 6, 2013
Published electronically: February 27, 2014
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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