טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentTamir Hemo
SubjectHomogeneous Asymptotic Limits of Uniform Averages on
Fuchsian Groups
DepartmentDepartment of Mathematics
Supervisor Full Professor Nevo Amos
Full Thesis textFull thesis text - English Version


Abstract

We study the distribution of matrix elements of discrete subgroups of the group of 2x2 unimodular matrices over the field of real numbers. Prominent examples are finitely generated subgroups of the group of 2x2 integral matrices.

For a non-elementary, geometrically finite group with critical exponent larger than 1/2, we demonstrate the equidistribution of homogeneous averages on the group taken in finite dimensional representations of the group of 2x2 unimodular matrices over the real numbers. The limit measure is given explicitly in terms of the representation and the Patterson-Sullivan measure corresponding to the discrete group.