期刊
ADVANCES IN MATHEMATICS
卷 287, 期 -, 页码 567-599出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.aim.2015.10.005
关键词
Quasimodular forms; Vector-valued modular forms; Weak Jacobi forms; Rankin-Cohen brackets
类别
资金
- University of Northern Iowa
- [NRF-2013R1A2A2A01068676]
- [NRF-2015049582]
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. (C) 2015 Elsevier Inc. All rights reserved.
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