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]
< Reduce
Harvard University
Lithe and fast algorithmic number theory [LFANT]
Analyse cryptographique et arithmétique [CANARI]
Language
en
Document de travail - Pré-publication
English Abstract
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 ...Read more >
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.Read less <
English Keywords
Abelian surfaces
Isogenies
Modular polynomials
Complexity
Origin
Hal imported