Hermitian Jacobi Forms of Higher Degree
| dc.contributor.advisor | Eischen, Ellen | |
| dc.contributor.author | Haight, Sean | |
| dc.date.accessioned | 2024-08-07T21:23:19Z | |
| dc.date.available | 2024-08-07T21:23:19Z | |
| dc.date.issued | 2024-08-07 | |
| dc.description.abstract | We develop the theory of Hermitian Jacobi forms in degree $n > 1$. This builds on the work of Klaus Haverkamp in \cite{HThesis} who developed this theory in degree $n = 1$. Haverkamp in turn generalized a monograph of Eichler and Zagier, \cite{E&Z}. Hermitian Jacobi forms are holomorphic functions which appear in certain infinite series expansions (Fourier Jacobi expansions) of Hermitian modular forms. In this work we give a definition of Hermitian Jacobi forms in degree $n > 1$, give their relationship to more classical Hermitian modular forms and construct a useful tool for studying Hermitian Jacobi forms, the theta expansion. This theta expansion allows us to relate our forms to classical modular forms via the Eichler-Zagier map and thereby bound the dimension of our space of forms. We then go on to apply the developed theory to prove some non-vanishing results on the Fourier coefficients of Hermitian modular forms. | en_US |
| dc.identifier.uri | https://hdl.handle.net/1794/29727 | |
| dc.language.iso | en_US | |
| dc.publisher | University of Oregon | |
| dc.rights | All Rights Reserved. | |
| dc.subject | Automorphic Forms | en_US |
| dc.subject | Hermitian Jacobi Forms | en_US |
| dc.subject | Jacobi Forms | en_US |
| dc.title | Hermitian Jacobi Forms of Higher Degree | |
| dc.type | Electronic Thesis or Dissertation | |
| thesis.degree.discipline | Department of Mathematics | |
| thesis.degree.grantor | University of Oregon | |
| thesis.degree.level | doctoral | |
| thesis.degree.name | Ph.D. |
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