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Computing classical modular forms as orthogonal modular forms

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Post-edited
Authors : Voight, John (Author of the conference)
CIRM (Publisher )

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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
Abstract : 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.

MSC Codes :
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
Additional resources :
http://www.cirm-math.fr/ProgWeebly/Renc1608/voight.pdf
    Information on the Video

    Film maker : Hennenfent, Guillaume
    Language : English
    Available date : 29/06/2017
    Conference Date : 21/06/2017
    Subseries : Research talks
    arXiv category : Number Theory
    Mathematical Area(s) : Algebraic & Complex Geometry ; Number Theory
    Format : MP4 (.mp4) - HD
    Video Time : 00:57:41
    Targeted Audience : Researchers
    Download : https://videos.cirm-math.fr/2017-06-21_Voight.mp4
Information on the Event

Event Title : AGCT - Arithmetic, Geometry, Cryptography and Coding Theory / AGCT - Arithmétique, géométrie, cryptographie et théorie des codes
Event Organizers : Aubry, Yves ; Howe, Everett ; Ritzenthaler, Christophe
Dates : 19/06/17 - 23/06/17
Event Year : 2017
Event URL : 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

See Also

Bibliography

  • 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


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