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.

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