Automorphic forms and the periods of abelian varieties

Periods of Abelian Varieties

We prove various characterizations of the period torsor of abelian varieties.

Closed Geodesics and Periods of Automorphic Forms

We study the detailed structure of the distribution of Eichler-Shimura periods of an automorphic form on a compact hyperbolic surface. We show that these periods do not cluster around the asymptotic period over a homology class discovered by Zelditch. 0. Introduction and Results Let M = H/Γ be a compact hyperbolic surface, where Γ is a discrete subgroup of PSL(2,R) = SL(2,R)/{±I}. Such a surfac...

2 Periods of Abelian Varieties

We prove various characterizations of the period torsor of abelian varieties, and we correct some errors in the literature. A shortened version of this paper will be submitted for publication.

Automorphic Forms on Shimura Varieties

Hyperbolicity, automorphic forms and Siegel modular varieties

We study the hyperbolicity of compactifications of quotients of bounded symmetric domains by arithmetic groups. We prove that, up to an étale cover, they are Kobayashi hyperbolic modulo the boundary. Applying our techniques to Siegel modular varieties, we improve some former results of Nadel on the non-existence of certain level structures on abelian varieties over complex function fields.