THE RAMANUJAN JOURNAL, Vol. 10, No. 3 (2005),
Generating Jacobi Forms
Received November 15, 2002; Accepted April 28, 2004
Abstract. In this paper we explore the relationship between vector-valued modular forms and Jacobi forms and give explicit relations over various congruence subgroups. The main result is that a Jacobi form of square-free index on the full Jacobi group is uniquely determined by any of the associated vector components. In addition, an explicit construction of a Jacobi form from a subset of its Fourier coefficients. This leads to results about how the transformation properties are affected by congruence restrictions on the Fourier expansion.
Keywords: Jacobi forms, vector-valued modular forms
Original article available at www.springerlink.com:
Sat Jul 8 10:51:44 EDT 2006