Higher order modular forms and mixed Hodge theory
arXiv:0909.0714 · doi:10.4064/aa139-4-2
Abstract
In this paper we introduce a certain space of higher order modular forms of weight 0 and show that it has a Hodge structure coming from the geometry of the fundamental group of a modular curve. This generalizes the usual structure on classical weight 2 forms coming from the cohomology of the modular curve. Further we construct some higher order Poincare series to get higher order higher weight forms and using them we define a space of higher weight, higher order forms which has a mixed Hodge structure as well.
26 pages. To appear in Acta Arithmetica. New version corrects issues with text being truncated