MATH Seminar
| Title: Maass forms and modular forms: applications to class numbers and partitions |
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| Defense: Dissertation |
| Speaker: Olivia Beckwith of Emory University |
| Contact: Olivia Beckwith, olivia.dorothea.beckwith@emory.edu |
| Date: 2018-04-02 at 3:00PM |
| Venue: W302 |
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| Abstract: This dissertation is about arithmetic information encoded by analytic characteristics (such as Fourier coefficients) of classical modular forms and a real-analytic generalization of modular forms called harmonic Maass forms. For example, I use the theory of harmonic Maass forms to extend and refine a theorem of Wiles on class number divisibility. I also prove asymptotic bounds for Rankin-Selberg shifted convolution L-functions in shift aspect. In partition theory, I use the circle method to describe the expected distribution of parts of integer partitions over residue classes, and I use effective estimates for partition functions to obtain simple formulas for functions arising in group theory. |
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