Published on *Max Planck Institute for Mathematics* (http://www.mpim-bonn.mpg.de)

Posted in

- Talk [1]

Speaker:

Martin Raum
Date:

Wed, 08/09/2010 - 14:15 - 15:15 We generalize Maass-Jacobi forms for indices in Z, hence lattices of rank 1, to Maass-Jacobi forms with index a lattice of arbitrary rank. PoincarĂ© series can be used to analyze the space of such functions. In particular, applying this technique we can prove a Zagier type duality. The dual weights coincide with the dual weights suggested for corresponding Maass-Siegel forms. A connection to the already known skew-holomorphic Jacobi forms is revealed by introducing an appropriate xi-operator. We also briefly discuss the underlying Lie algebra and its universal enveloping algebra. Here the situation is much more involved than in the rank 1 case.

**Links:**

[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39

[2] http://www.mpim-bonn.mpg.de/node/3444

[3] http://www.mpim-bonn.mpg.de/node/246