2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/102284We 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.24 pages, 2 figures. Changes: Include a reference to a preprint of Collier and Sharp where they apply our techniques to variable curvature. Corrected a lemma which Collier and Sharp pointed out was wrong. Our main theorem changed accordinglyNumber Theory05C25; 20F69, 37D40, 11M36text