Faculty Publications

Title

Symmetric tensor representations, quasimodular forms, and weak Jacobi forms

Document Type

Article

Keywords

Quasimodular forms, Rankin-Cohen brackets, Vector-valued modular forms, Weak Jacobi forms

Journal/Book/Conference Title

Advances in Mathematics

Volume

287

First Page

567

Last Page

599

Abstract

We establish a correspondence between vector-valued modular forms with respect to a symmetric tensor representation and quasimodular forms. This is carried out by first obtaining an explicit isomorphism between the space of vector-valued modular forms with respect to a symmetric tensor representation and the space of finite sequences of modular forms of certain type. This isomorphism uses Rankin-Cohen brackets and extends a result of Kuga and Shimura, who considered the case of vector-valued modular forms of weight two. We also obtain a correspondence between such vector-valued modular forms and weak Jacobi forms.

Original Publication Date

1-10-2016

DOI of published version

10.1016/j.aim.2015.10.005

Repository

UNI ScholarWorks, Rod Library, University of Northern Iowa

Language

en

Share

COinS