Modular polynomials on Hilbert surfaces
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en
Article de revue
Este ítem está publicado en
Journal of Number Theory. 2020-05, vol. 216, p. 403-459
Elsevier
Resumen en inglés
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 ...Leer más >
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.< Leer menos
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