Hilbert Modular Polynomials
| hal.structure.identifier | Universiteit Leiden = Leiden University | |
| hal.structure.identifier | Lithe and fast algorithmic number theory [LFANT] | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | MARTINDALE, Chloe | |
| dc.date.accessioned | 2024-04-04T03:02:20Z | |
| dc.date.available | 2024-04-04T03:02:20Z | |
| dc.date.issued | 2020 | |
| dc.identifier.issn | 0022-314X | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/192971 | |
| dc.description.abstractEn | We present an algorithm to compute a higher dimensional analogue of modular polynomials. This higher dimensional analogue, the 'set of Hilbert modular polynomials', concerns cyclic isogenies of principally polarised abelian varieties with maximal real multiplication by a fixed totally real number field K0. We give a proof that this algorithm is correct, and provide practical improvements and an implementation for the 2-dimensional case with K0 = Q(√ 5). We also explain applications of this algorithm to point counting, walking on isogeny graphs, and computing class polynomials. | |
| dc.language.iso | en | |
| dc.publisher | Elsevier | |
| dc.subject.en | Hilbert modular polynomials | |
| dc.subject.en | Cyclic isogenies | |
| dc.subject.en | Abelian varieties | |
| dc.subject.en | Genus two | |
| dc.subject.en | Maximal real multiplication | |
| dc.title.en | Hilbert Modular Polynomials | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1016/j.jnt.2019.11.019 | |
| dc.subject.hal | Mathématiques [math]/Théorie des nombres [math.NT] | |
| bordeaux.journal | Journal of Number Theory | |
| bordeaux.page | 464-498 | |
| bordeaux.volume | 213 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01990298 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01990298v1 | |
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