Modular polynomials on Hilbert surfaces
Language
en
Article de revue
This item was published in
Journal of Number Theory. 2020-05, vol. 216, p. 403-459
Elsevier
English Abstract
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 ...Read more >
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.Read less <
Origin
Hal imported