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Chapitres

Computing classical modular forms as orthogonal modular forms

Apparaît dans la collection : Arithmetic, Geometry, Cryptography and Coding Theory / Arithmétique, géométrie, cryptographie et théorie des codes

Birch gave an extremely efficient algorithm to compute a certain subspace of classical modular forms using the Hecke action on classes of ternary quadratic forms. We extend this method to compute all forms of non-square level using the spinor norm, and we exhibit an implementation that is very fast in practice. This is joint work with Jeffery Hein and Gonzalo Tornaria.

Informations sur la vidéo

Date de captation 21/06/2017
Date de publication 29/06/2017
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Réalisateur(s) Guillaume Hennenfent
Format MP4

Données de citation

DOI 10.24350/CIRM.V.19185803
Citer cette vidéo Voight, John (21/06/2017). Computing classical modular forms as orthogonal modular forms. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19185803
URL https://dx.doi.org/10.24350/CIRM.V.19185803

Domaine(s)

Théorie des nombres

Bibliographie

Birch, B.J. (1991). Hecke actions on classes of ternary quadratic forms. In A. Pethö, M.E. Pohst, H.C. Williams & H.G. Zimmer (Eds.), Computational number theory : proceedings of the colloquium on computational number theory held at Kossuth Lajos University, Debrecen (Hungary), September 4-9, 1989 (pp. 191-212). Berlin: de Gruyter - https://www.zbmath.org/?q=an:0748.11023
Hein, J. (2016). Orthogonal modular forms: An application to a conjecture of birch, algorithms and computations (Order No. 10145500). ProQuest Dissertations & Theses Global - http://gradworks.umi.com/10/14/10145500.html

Codes MSC

Document(s)

http://www.cirm-math.fr/ProgWeebly/Renc1608/voight.pdf

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