Faculty Publications

Vector-Valued Jacobi-Like Forms

Document Type

Article

Keywords

Jacobi-like forms, Modular forms, Rankin-Cohen brackets

Journal/Book/Conference Title

Monatshefte fur Mathematik

Volume

152

Issue

4

First Page

321

Last Page

336

Abstract

We introduce vector-valued Jacobi-like forms associated to a representation ρ : Γ → GL(n, ℂ) of a discrete subgroup Γ ⊂ SL(2, ℂ) in ℂn and establish a correspondence between such vector-valued Jacobi-like forms and sequences of vector-valued modular forms of different weights with respect to ρ. We determine a lifting of vector-valued modular forms to vector-valued Jacobi-like forms as well as a lifting of scalar-valued Jacobi-like forms to vector-valued Jacobi-like forms. We also construct Rankin-Cohen brackets for vector-valued modular forms. © 2007 Springer-Verlag.

Department

Department of Mathematics

Original Publication Date

12-1-2007

DOI of published version

10.1007/s00605-007-0466-4

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