Mathematical Research Letters
Volume 14 (2007)
Maass-Jacobi forms over complex quadratic fields
Pages: 137 – 156
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.