Equidistribution of geodesics on homology classes and analogues for free groups
by Yiannis N. Petridis and Morten S. Risager
Preprints
Number 14 (September 2005)
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 a random set of homology classes and certain arithmetic sets. We explain the analogues for free groups, conjugacy classes and discrete logarithms, in particular, we investigate the density of conjugacy classes with relatively prime discrete logarithms.