Dissertations, Theses, and Capstone Projects
Date of Degree
9-2019
Document Type
Dissertation
Degree Name
Ph.D.
Program
Mathematics
Advisor
Krzysztof Klosin
Committee Members
Kenneth Kramer
Brooke Feigon
Subject Categories
Number Theory
Keywords
modular forms, Hermitian modular forms, Maass lift, Saito-Kurokawa lift
Abstract
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.
Recommended Citation
Vu, An Hoa, "Hermitian Maass Lift for General Level" (2019). CUNY Academic Works.
https://academicworks.cuny.edu/gc_etds/3355