Open Access
VOL. 6 | 2005 Dimension Formulas for Automorphic Forms of Coabelian Hyperbolic Type
Rolf-Peter Holzapfel

Editor(s) Ivaïlo M. Mladenov, Allen C. Hirshfeld

Geom. Integrability & Quantization, 2005: 240-251 (2005) DOI: 10.7546/giq-6-2005-240-251


There are infinitely many hyperbolic transforms of complex abelian surfaces. The corresponding universal covers change from the complex plane to the unit ball, from flat to hyperbolic metrics. Looking back to Jacobi’s periodic functions we were able to construct 2-dimensional abelian functions transformable to automorphic forms on the ball. In this article we prove explicit dimension formulas for all forms of this coabelian types for fixed weights.


Published: 1 January 2005
First available in Project Euclid: 12 June 2015

zbMATH: 1093.14033
MathSciNet: MR2161771

Digital Object Identifier: 10.7546/giq-6-2005-240-251

Rights: Copyright © 2005 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences


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