THE RAMANUJAN JOURNAL, Vol. 10, No. 3 (2005), 325-339.

Generating Jacobi Forms

HOWARD SKOGMAN
Department of Mathematics, SUNY Brockport, Brockport, New York 14420
Email: hskogman@brockport.edu
Homepage: http://www.acs.brockport.edu/~hskogman/

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

2000 Mathematics Classification: Primary 11F50; Secondary 11F30