Modular polynomials on Hilbert surfaces
Langue
en
Article de revue
Ce document a été publié dans
Journal of Number Theory. 2020-05, vol. 216, p. 403-459
Elsevier
Résumé en anglais
We describe an evaluation/interpolation approach to compute modular polynomials on a Hilbert surface, which parametrizes abelian surfaces with maximal real multiplication. Under some heuristics we obtain a quasi-linear ...Lire la suite >
We describe an evaluation/interpolation approach to compute modular polynomials on a Hilbert surface, which parametrizes abelian surfaces with maximal real multiplication. Under some heuristics we obtain a quasi-linear algorithm. The corresponding modular polynomials are much smaller than the ones on the Siegel threefold. We explain how to compute even smaller polynomials by using pullbacks of theta functions to the Hilbert surface.< Réduire
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