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5 papers · 2 filters
Equidistribution of geodesics on homology classes and analogues for free groups
Yiannis Petridis, Morten S. Risager
We investigate how often geodesics have homology in a fixed set of the homology lattice of a compact Riemann surface. We prove that closed geodesics are equidistributed on any sets…
Iterated Shimura integrals
Yu. I. Manin
In this paper I continue the study of iterated integrals of modular forms and noncommutative modular symbols for started in [Ma3]. Main new results involv…
Friendly measures, homogeneous flows and singular vectors
Dmitry Kleinbock, Barak Weiss
We prove that singular vectors have measure zero with respect to any friendly measure on (e.g. the volume measure on a nondegenerate submanifold). This generalizes speci…
Flows on -arithmetic homogeneous spaces and applications to metric Diophantine approximation
Dmitry Kleinbock, George Tomanov
The main goal of this work is to establish quantitative nondivergence estimates for flows on homogeneous spaces of products of real and -adic Lie groups. These results have appl…
Differential equations satisfied by modular forms and K3 surfaces
Yifan Yang, Noriko Yui
We study differential equations satisfied by modular forms associated to , where are genus zero subgroups of commensurable with $SL_2(…