Modular polynomials on Hilbert surfaces
| hal.structure.identifier | Cryptology, arithmetic : algebraic methods for better algorithms [CARAMBA] | |
| dc.contributor.author | MILIO, Enea | |
| hal.structure.identifier | Lithe and fast algorithmic number theory [LFANT] | |
| dc.contributor.author | ROBERT, Damien | |
| dc.date.accessioned | 2024-04-04T02:57:49Z | |
| dc.date.available | 2024-04-04T02:57:49Z | |
| dc.date.created | 2019-06-30 | |
| dc.date.issued | 2020-05 | |
| dc.identifier.issn | 0022-314X | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/192596 | |
| dc.description.abstractEn | We describe an evaluation/interpolation approach to compute modular polynomials on a Hilbert surface, which parametrizes abelian surfaces with maximal real multiplication. Under some heuristics we obtain a quasi-linear algorithm. The corresponding modular polynomials are much smaller than the ones on the Siegel threefold. We explain how to compute even smaller polynomials by using pullbacks of theta functions to the Hilbert surface. | |
| dc.language.iso | en | |
| dc.publisher | Elsevier | |
| dc.rights.uri | http://creativecommons.org/licenses/by/ | |
| dc.title.en | Modular polynomials on Hilbert surfaces | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1016/j.jnt.2020.04.014 | |
| dc.subject.hal | Mathématiques [math] | |
| bordeaux.journal | Journal of Number Theory | |
| bordeaux.page | 403-459 | |
| bordeaux.volume | 216 | |
| 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-01520262 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01520262v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Journal%20of%20Number%20Theory&rft.date=2020-05&rft.volume=216&rft.spage=403-459&rft.epage=403-459&rft.eissn=0022-314X&rft.issn=0022-314X&rft.au=MILIO,%20Enea&ROBERT,%20Damien&rft.genre=article |
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