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]
< Leer menos
Harvard University
Lithe and fast algorithmic number theory [LFANT]
Analyse cryptographique et arithmétique [CANARI]
Idioma
en
Document de travail - Pré-publication
Resumen en inglés
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 ...Leer más >
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.< Leer menos
Palabras clave en inglés
Abelian surfaces
Isogenies
Modular polynomials
Complexity
Orígen
Importado de HalCentros de investigación