Faculty Publications
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.
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
