University of North Texas 
Master's and Doctoral Defenses
Learn about the exciting research our graduate students are preparing to defend in their final steps toward earning their degree in mathematics.
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February 27, 2026: Erin Pierce, PhDTitle: On Siegel Eisenstein Series with LevelAbstract: Siegel modular forms are higher-dimensional analogues of classical modular forms and play an important role in modern number theory, connecting arithmetic geometry, representation theory, and the Langlands program. They can be viewed as automorphic forms on symplectic groups and encode deep arithmetic information through their Fourier coefficients and associated L-functions. In this defense, we will introduce a specific type of Siegel modular form called an Eisenstein series. In particular, we will use representation theoretic methods to construct an Eisenstein series derived from the Siegel parabolic subgroup of GSp(4), corresponding to a Siegel modular form with paramodular level. We will discuss the adelic method for computing its Fourier coefficients, present a novel approach for calculating them, and explain why they live in a particular number field. |
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