Mathematical Research Letters

Volume 14 (2007)

Number 1

Maass-Jacobi forms over complex quadratic fields

Pages: 137 – 156

DOI: http://dx.doi.org/10.4310/MRL.2007.v14.n1.a12

Authors

Kathrin Bringmann (University of Minnesota)

Charles H. Conley (University of North Texas)

Olav K. Richter (University of North Texas)

Abstract

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.

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