Skip to Main content Skip to Navigation
Journal articles

Modular polynomials on Hilbert surfaces

Enea Milio 1 Damien Robert 2
1 CARAMBA - Cryptology, arithmetic : algebraic methods for better algorithms
Inria Nancy - Grand Est, LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry
2 LFANT - Lithe and fast algorithmic number theory
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
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 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.
Document type :
Journal articles
Complete list of metadatas

Cited literature [73 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01520262
Contributor : Damien Robert <>
Submitted on : Thursday, January 9, 2020 - 12:58:48 PM
Last modification on : Monday, June 8, 2020 - 2:53:22 PM

File

revisionHilbert.pdf
Files produced by the author(s)

Identifiers

Collections

Citation

Enea Milio, Damien Robert. Modular polynomials on Hilbert surfaces. Journal of Number Theory, Elsevier, 2020, ⟨10.1016/j.jnt.2020.04.014⟩. ⟨hal-01520262v3⟩

Share

Metrics

Record views

116

Files downloads

93