Distribution of infinite geodesics on a modular surface and a skew product from Gauss map

Abstract

This is a research in progress. We begin the talk by introducing the problem of distribution of modular symbols in the homology group of modular curves, which can be regarded as an infinite length version of the famous theorem on the distribution of closed geodesics on a hyperbolic manifold. After the introduction, we present how to relate the problem to a study on the transfer operator of skew product of the Gauss map and a map on the left cosets of in Numerical evidences are also to be presented.