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Speaker:

Martin Raum
Date:

Wed, 2010-09-08 14:15 - 15:15
Location:

MPIM Lecture Hall
Parent event:

Number theory lunch seminar 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. Poincaré 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.

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