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H 2 Computing classical modular forms as orthogonal modular forms

Auteurs : Voight, John (Auteur de la Conférence)
CIRM (Editeur )

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quadratic forms and lattices isometries and genus neighbors orthogonal modular forms and Hecke action Birch theorem Even Clifford algebra weight spinor norm Hecke operator supersingular elliptic curves

Résumé : 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.

Codes MSC :
11E20 - General ternary and quaternary quadratic forms; forms of more than two variables
11F11 - Holomorphic modular forms of integral weight
11F27 - Theta series; Weil representation; theta correspondences
11F37 - Forms of half-integer weight; nonholomorphic modular forms

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

    Informations sur la Vidéo

    Réalisateur : Hennenfent, Guillaume
    Langue : Anglais
    Date de publication : 29/06/17
    Date de captation : 21/06/17
    Collection : Research talks
    Format : MP4 (.mp4) - HD
    Durée : 00:57:41
    Domaine : Algebraic & Complex Geometry ; Number Theory
    Audience : Chercheurs ; Doctorants , Post - Doctorants
    Download : http://videos.cirm-math.fr/2017-06-21_Voight.mp4

Informations sur la rencontre

Nom du congrès : Arithmetic, geometry, cryptography and coding theory / Arithmétique, géométrie, cryptographie et théorie des codes
Organisteurs Congrès : Aubry, Yves ; Howe, Everett ; Ritzenthaler, Christophe
Dates : 19/06/17 - 23/06/17
Année de la rencontre : 2017
URL Congrès : http://conferences.cirm-math.fr/1608.html

Citation Data

DOI : 10.24350/CIRM.V.19185803
Cite this video as: Voight, John (2017). Computing classical modular forms as orthogonal modular forms. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19185803
URI : http://dx.doi.org/10.24350/CIRM.V.19185803

Voir aussi

Bibliographie

  1. 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

  2. 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



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