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

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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 ... continued below

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Martin, James D December 2016.

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  • Martin, James D

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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.

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  • December 2016

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  • Feb. 19, 2017, 7:42 p.m.

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Martin, James D. Rankin-Cohen Brackets for Hermitian Jacobi Forms and Hermitian Modular Forms, dissertation, December 2016; Denton, Texas. (digital.library.unt.edu/ark:/67531/metadc955117/: accessed October 15, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .