  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 with asymptotic density with respect to a
specific norm. 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.
