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Modular polynomials on Hilbert surfaces

hal.structure.identifierCryptology, arithmetic : algebraic methods for better algorithms [CARAMBA]
dc.contributor.authorMILIO, Enea
hal.structure.identifierLithe and fast algorithmic number theory [LFANT]
dc.contributor.authorROBERT, Damien
dc.date.accessioned2024-04-04T02:57:49Z
dc.date.available2024-04-04T02:57:49Z
dc.date.created2019-06-30
dc.date.issued2020-05
dc.identifier.issn0022-314X
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/192596
dc.description.abstractEnWe 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.isoen
dc.publisherElsevier
dc.rights.urihttp://creativecommons.org/licenses/by/
dc.title.enModular polynomials on Hilbert surfaces
dc.typeArticle de revue
dc.identifier.doi10.1016/j.jnt.2020.04.014
dc.subject.halMathématiques [math]
bordeaux.journalJournal of Number Theory
bordeaux.page403-459
bordeaux.volume216
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-01520262
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01520262v1
bordeaux.COinSctx_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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