Hermitian Maass Lift for General Level

<p>For an imaginary quadratic field $K$ of discriminant $-D$, let \chi = \chi_K be the associated quadratic character. We will show that the space of special hermitian Jacobi forms of level $N$ is isomorphic to the space of plus forms of level $DN$ and nebentypus $\chi$ (the hermitian analogue of Kohnen's plus space) for any integer $N$ prime to $D$. This generalizes the results of Krieg from $N = 1$ to arbitrary level. Combining this isomorphism with the recent work of Berger and Klosin and a modification of Ikeda's construction we prove the existence of a lift from the space of elliptic modular forms to the space of hermitian modular forms of level $N$ which can be viewed as a generalization of the classical hermitian Maass lift to arbitrary level.</p>

Name thesis:degree_name

Doctor of Philosophy

Level thesis:degree_level

Doctoral

Discipline thesis:degree_discipline

Mathematics

Grantor

The Graduate School and University Center of The City University of New York

Year dc:date.available

2019

Author dc:creator

• Vu, An Hoa

Advisor dc:contributor.advisor

• Krzysztof Klosin

Committee members dc:contributor.committeemember

• Kenneth Kramer
• Brooke Feigon

• Number Theory
• modular forms
• Hermitian modular forms
• Maass lift
• Saito-Kurokawa lift

Repository record dc:identifier

https://academicworks.cuny.edu/gc_etds/3355

OAI identifier oai:identifier

oai:academicworks.cuny.edu:gc_etds-4426