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http://hdl.handle.net/11375/29029
Title: | Vector Valued Modular Forms of Dimension $3$ |
Authors: | Virk, Gagandeep |
Advisor: | Franc, Cameron |
Department: | Mathematics and Statistics |
Keywords: | Thesis;PhD Thesis |
Publication Date: | 2023 |
Abstract: | In this thesis we describe and relate various representations of $3$-dimensional vector valued modular forms. In particular, we give algebraic formulas for families of $3$-dimensional vector valued modular forms on $\Gamma_0(2)$, a subgroup of the modular group $\Gamma = SL_2(\mathbb{Z})$. These formulas enable us to compute CM values of the $3$-dimensional vector valued modular forms at CM points in the upper half plane. We also define families of Eisenstein series corresponding to one-dimensional representation, $\chi$, on $\Gamma_0(2)$. This gives a different description of the algebraic family discussed in the preceding paragraph. For Eisenstein series of weight $4$ and $6$, we evaluate their Fourier series expansion and compute their Fourier coefficients. The constant term in the Fourier series expansion of Eisenstein series of weight $4$ and $6$ is then expressed using Bessel function of the first kind and Kloosterman sums. |
URI: | http://hdl.handle.net/11375/29029 |
Appears in Collections: | Open Access Dissertations and Theses |
Files in This Item:
File | Description | Size | Format | |
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Virk_Gagandeep_K_2023 Sep_PhD.pdf | 506.88 kB | Adobe PDF | View/Open |
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