English
Computing classical modular forms as orthogonal modular forms
Post-edited
Auteurs : Voight, John (Auteur de la Conférence)
CIRM (Editeur )
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
CIRM (Editeur )
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, GuillaumeLangue : Anglais Date de publication : 29/06/2017 Date de captation : 21/06/2017 Sous collection : Research talks arXiv category : Number Theory Domaine : Algebraic & Complex Geometry ; Number Theory Format : MP4 (.mp4) - HD Durée : 00:57:41 Audience : Researchers Download : https://videos.cirm-math.fr/2017-06-21_Voight.mp4 
|
Informations sur la Rencontre
Nom de la rencontre : AGCT - Arithmetic, Geometry, Cryptography and Coding Theory / AGCT - Arithmétique, géométrie, cryptographie et théorie des codesOrganisateurs de la rencontre : 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
Données de citation
DOI : 10.24350/CIRM.V.19185803Citer cette vidéo: 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
- [Multi angle] Local densities compute isogeny classes / Auteur de la Conférence Achter, Jeffrey.
- [Multi angle] Maps between curves and diophantine obstructions / Auteur de la Conférence Voloch, José Felipe.
- [Multi angle] Brauer-Siegel theorem and analogues for varieties over global fields / Auteur de la Conférence Hindry, Marc.
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
