Symmetric Tensor Representations, Quasimodular Forms, And Weak Jacobi Forms

Authors

Young Ju Choie, Pohang University of Science and TechnologyFollow
Min Ho Lee, University of Northern IowaFollow

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.

Department

Department of Mathematics

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

Recommended Citation

Choie, Young Ju and Lee, Min Ho, "Symmetric Tensor Representations, Quasimodular Forms, And Weak Jacobi Forms" (2016). Faculty Publications. 1129.
https://scholarworks.uni.edu/facpub/1129