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Rankin-Cohen Brackets for Hermitian Jacobi Forms and Hermitian Modular Forms

In this thesis, we define differential operators for Hermitian Jacobi forms and Hermitian modular forms over the Gaussian number field Q(i). In particular, we construct Rankin-Cohen brackets for such spaces of Hermitian Jacobi forms and Hermitian modular forms. As an application, we extend Rankin's method to the case of Hermitian Jacobi forms. Finally we compute Fourier series coefficients of Hermitian modular forms, which allow us to give an example of the first Rankin-Cohen bracket of two Hermitian modular forms. In the appendix, we provide tables of Fourier series coefficients of Hermitian modular forms and also the computer source code that we used to compute such Fourier coefficients.

Identiferoai:union.ndltd.org:unt.edu/info:ark/67531/metadc955117
Date12 1900
CreatorsMartin, James D. (James Dudley)
ContributorsRichter, Olav K., Cherry, William, 1966-, Conley, Charles H.
PublisherUniversity of North Texas
Source SetsUniversity of North Texas
LanguageEnglish
Detected LanguageEnglish
TypeThesis or Dissertation
Formatv, 49 pages : illustrations, Text
RightsPublic, Martin, James D. (James Dudley), Copyright, Copyright is held by the author, unless otherwise noted. All rights Reserved.

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