Higher order modular forms and mixed Hodge theory
Number Theory
2015-05-14 v2 Algebraic Geometry
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.
Keywords
Cite
@article{arxiv.0909.0714,
title = {Higher order modular forms and mixed Hodge theory},
author = {Ramesh Sreekantan},
journal= {arXiv preprint arXiv:0909.0714},
year = {2015}
}
Comments
26 pages. To appear in Acta Arithmetica. New version corrects issues with text being truncated