Super Automorphic Forms on the Super Upper Half Plane
Complex Variables
2012-08-16 v3 Functional Analysis
Abstract
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.
Cite
@article{arxiv.0908.4566,
title = {Super Automorphic Forms on the Super Upper Half Plane},
author = {Roland Knevel},
journal= {arXiv preprint arXiv:0908.4566},
year = {2012}
}
Comments
36 pages, no figures, minor changes and improvement of the results