Dissertations, Theses, and Capstone Projects

9-2019

Dissertation

Ph.D.

Mathematics

Krzysztof Klosin

Kenneth Kramer

Brooke Feigon

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.

This work is embargoed and will be available for download on Thursday, September 30, 2021