Evaluating modular equations for abelian surfaces
KIEFFER, Jean
Harvard University
Lithe and fast algorithmic number theory [LFANT]
Analyse cryptographique et arithmétique [CANARI]
Harvard University
Lithe and fast algorithmic number theory [LFANT]
Analyse cryptographique et arithmétique [CANARI]
KIEFFER, Jean
Harvard University
Lithe and fast algorithmic number theory [LFANT]
Analyse cryptographique et arithmétique [CANARI]
< Réduire
Harvard University
Lithe and fast algorithmic number theory [LFANT]
Analyse cryptographique et arithmétique [CANARI]
Langue
en
Document de travail - Pré-publication
Résumé en anglais
We design algorithms to efficiently evaluate modular equations of Siegel and Hilbert type for abelian surfaces over number fields using complex approximations. Their output can be made provably correct if an explicit ...Lire la suite >
We design algorithms to efficiently evaluate modular equations of Siegel and Hilbert type for abelian surfaces over number fields using complex approximations. Their output can be made provably correct if an explicit description of the associated graded ring of modular forms over Z is known; this includes the Siegel case, and the Hilbert case for the quadratic fields of discriminant 5 and 8. Our algorithms also apply to finite fields via lifting.< Réduire
Mots clés en anglais
Abelian surfaces
Isogenies
Modular polynomials
Complexity
Origine
Importé de halUnités de recherche