We study modular forms, Jacobi forms, and hermitian formal Fourier-Jacobi series over imaginary quadratic fields. In the first section, we prove that the ring of classical Jacobi forms of a fixed genus g, varying index m and weight k is generated by theta functions. From this result we show that ring of classical Jacobi forms of bounded relative index is a finitely generated bigraded ring. In the second section, we study vector-valued hermitian modular forms and vector-valued hermitian Jacobi forms. In the last section we introduce the her mitian formal Fourier-Jacobi series. We show that hermitian formal Fourier Jacobi series form a finitely generated module over the ring of classical modular forms.

Creator

• Wang, Yuxiang

DOI

• https://doi.org/10.21985/n2-ream-pg77

Subject

• Mathematics

Language

• en

Alternate Identifier

• http://dissertations.umi.com/northwestern:15220
• etdadmin_upload_761403

Keyword

• Fourier Jacobi Expansion
• Modular Form
• Algebraic Number Theory

Date created

• 2020-01-01

Resource type

• Dissertation

Rights statement

• In Copyright