Super Automorphic Forms on the Super Upper Half Plane

Details Super Automorphic Forms on the Super Upper Half Plane Super Automorphic Forms on the Super Upper Half Plane

2009-08-31

arxiv.org/abs/0908.4566v2

Mathematics

Complex Variables

41 pages, no figures, minor changes and improvement of the results

Scientific paper

The super upper half plane, this is the ordinary upper half plane with additional odd (anticommuting) directions, admits a transitive super action of a certain super Lie group G . First we define the spaces of super automorphic and cusp forms on the super upper half plane for an ordinary lattice in G and give an asymptotic formula for their dimensions for high weight. For involving also the odd directions of G we introduce local super deformation of lattices in G and show that for high weight the spaces of super automorphic and cusp forms are stable under such local super deformations.

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