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H 1 Generators for the group of modular units for $\Gamma^1(N)$ over the rationals

Auteurs : Streng, Marco (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : The modular curve $Y^1(N)$ parametrises pairs $(E,P)$, where $E$ is an elliptic curve and $P$ is a point of order $N$ on $E$, up to isomorphism. A unit on the affine curve $Y^1(N)$ is a holomorphic function that is nowhere zero and I will mention some applications of the group of units in the talk.
    The main result is a way of generating generators (sic) of this group using a recurrence relation. The generators are essentially the defining equations of $Y^1(N)$ for $n < (N + 3)/2$. This result proves a conjecture of Maarten Derickx and Mark van Hoeij.

    Codes MSC :
    11B37 - Recurrences [For applications to special functions, see 33-XX]
    11B39 - Fibonacci and Lucas numbers and polynomials and generalizations
    11F03 - Modular and automorphic functions
    11G16 - Elliptic and modular units [See also 11R27]
    14H52 - Elliptic curves

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 04/06/15
      Date de captation : 18/05/15
      Collection : Research talks ; Algebraic and Complex Geometry ; Number Theory
      Format : quicktime ; audio/x-aac
      Durée : 00:27:47
      Domaine : Number Theory ; Algebraic & Complex Geometry
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2015-05-18_Streng.mp4

    Informations sur la rencontre

    Nom de la rencontre : Arithmetics, geometry, cryptography and coding theory / Arithmétique, géométrie, cryptographie et théorie des codes
    Organisateurs de la rencontre : Bassa, Alp ; Couvreur, Alain ; Kohel, David
    Dates : 18/05/15 - 22/05/15
    Année de la rencontre : 2015
    URL Congrès : http://conferences.cirm-math.fr/1193.html

    Citation Data

    DOI : 10.24350/CIRM.V.18766003
    Cite this video as: Streng, Marco (2015). Generators for the group of modular units for $\Gamma^1(N)$ over the rationals. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18766003
    URI : http://dx.doi.org/10.24350/CIRM.V.18766003


    Bibliographie

    1. Streng, M. (2015). Generators of the group of modular units for $\Gamma^1(N)$ over $\mathbf{Q}$. - http://arxiv.org/abs/1503.08127

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