Universität zu Köln

Harmonic Maass Forms, Jacobi Forms, and Applications to Lie Superalgebras

Olivetto, René (2014) Harmonic Maass Forms, Jacobi Forms, and Applications to Lie Superalgebras. PhD thesis, Universität zu Köln.

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    Abstract

    In this thesis, we prove several results concerning the shape, the modular properties, and the asymptotic behavior of the Fourier coefficients of meromorphic Jacobi forms, with applications to Lie superalgebras. By work of Kac and Wakimoto, Bringmann and Ono, Bringmann and Folsom, and Bringmann, Folsom, and Mahlburg it is known that the generating functions of Kac-Wakimoto characters relative to the $\sl(m|n)^\wedge$ superalgebra are essentially meromorphic Jacobi forms. Extending previous work of Bringmann and Folsom, we investigate Kac-Wakimoto characters for any choice of integers $m>n>0$. Subsequently, we extend the study to any single-variable meromorphic Jacobi form of positive index, and to multivariable Kac-Wakimoto characters. Finally, we investigate the asymptotic behavior of the Fourier coefficients of single-variable Kac-Wakimoto characters using a generalization of the Hardy-Ramanujan Circle Method.

    Item Type: Thesis (PhD thesis)
    Creators:
    CreatorsEmail
    Olivetto, Renérene87@live.it
    URN: urn:nbn:de:hbz:38-58346
    Subjects: Mathematics
    Uncontrolled Keywords:
    KeywordsLanguage
    Modular forms , mock modular forms, Jacobi forms, Lie superalgebras, Kac-Wakimoto charactersEnglish
    Faculty: Mathematisch-Naturwissenschaftliche Fakultät
    Divisions: Mathematisch-Naturwissenschaftliche Fakultät > Mathematisches Institut
    Language: English
    Date: 10 July 2014
    Date Type: Publication
    Date of oral exam: 01 September 2014
    Full Text Status: Public
    Date Deposited: 05 Jan 2015 15:35:15
    Referee
    NameAcademic Title
    Bringmann, KathrinProf. Dr.
    Zwegers, SanderProf. Dr.
    URI: http://kups.ub.uni-koeln.de/id/eprint/5835

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