Dimension Formulas for Automorphic Forms of Coabelian Hyperbolic Type

Abstract

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.