Pré-Publication, Document De Travail Année : 2017

Modular polynomials on Hilbert surfaces

Résumé

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, and give an application to the CRT method to construct class polynomials.

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Dates et versions

hal-01520262 , version 1 (10-05-2017)
hal-01520262 , version 2 (09-09-2017)
hal-01520262 , version 3 (09-01-2020)

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  • HAL Id : hal-01520262 , version 2

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Enea Milio, Damien Robert. Modular polynomials on Hilbert surfaces. 2017. ⟨hal-01520262v2⟩
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