- Richard M. Hain. The geometry of the mixed Hodge structure on the fundamental group. In Algebraic geometry, Bowdoin
- Maine, 1985), volume 46 of Proc. Sympos. Pure…
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 generalises the usual structure on classical weight 2 forms coming from the cohomology of the modular curve. Further we construct some higher order Poincaré 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. Mathematics Subject Classication (2000) : 11F11, 14C30, 30F30, 32S35.