Mathematical Research Letters

Volume 14, Issue 1, January 2007 pp. 137-156.

Maass-Jacobi forms over complex quadratic fields

Authors: Kathrin Bringmann (1), Charles H. Conley (2), and Olav K. Richter (3)
Author institution: University of Minnesota (1), University of North Texas (2), University of North Texas (3)

Summary: We use methods from representation theory and invariant theory to compute differential operators invariant under the action of the Jacobi group over a complex quadratic field. This allows us to introduce Maass-Jacobi forms over complex quadratic fields, which are Jacobi forms that are also eigenfunctions of an invariant differential operator. We present explicit examples via Jacobi-Eisenstein series.

Contents Full-Text PDF