Evaluating Igusa functions
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- by Reinier Bröker and Kristin Lauter PDF
- Math. Comp. 83 (2014), 2977-2999 Request permission
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.References
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Additional Information
- Reinier Bröker
- Affiliation: Brown University, Box 1917, 151 Thayer Street, Providence, Rhode Island 02912
- MR Author ID: 759393
- Email: reinier@math.brown.edu
- Kristin Lauter
- Affiliation: Microsoft Research, One Microsoft Way, Redmond, Washington 98052
- MR Author ID: 619019
- ORCID: 0000-0002-1320-696X
- Email: klauter@microsoft.com
- 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
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 83 (2014), 2977-2999
- MSC (2010): Primary 11F46; Secondary 14J15
- DOI: https://doi.org/10.1090/S0025-5718-2014-02816-0
- MathSciNet review: 3246819