Evaluating modular equations for abelian surfaces
| hal.structure.identifier | Harvard University | |
| hal.structure.identifier | Lithe and fast algorithmic number theory [LFANT] | |
| hal.structure.identifier | Analyse cryptographique et arithmétique [CANARI] | |
| dc.contributor.author | KIEFFER, Jean | |
| dc.date.accessioned | 2024-04-04T02:41:59Z | |
| dc.date.available | 2024-04-04T02:41:59Z | |
| dc.date.created | 2020-10-19 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/191202 | |
| dc.description.abstractEn | 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. | |
| dc.language.iso | en | |
| dc.subject.en | Abelian surfaces | |
| dc.subject.en | Isogenies | |
| dc.subject.en | Modular polynomials | |
| dc.subject.en | Complexity | |
| dc.title.en | Evaluating modular equations for abelian surfaces | |
| dc.type | Document de travail - Pré-publication | |
| dc.subject.hal | Mathématiques [math]/Théorie des nombres [math.NT] | |
| dc.identifier.arxiv | 2010.10094 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| hal.identifier | hal-02971326 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-02971326v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=KIEFFER,%20Jean&rft.genre=preprint |
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