Equidistribution of geodesics on homology classes and analogues for free groups

Details Equidistribution of geodesics on homology classes and analogues for free groups Equidistribution of geodesics on homology classes and analogues for free groups

2005-09-22

arxiv.org/abs/math/0509513v3

Mathematics

Number Theory

24 pages, 2 figures. Changes: Include a reference to a preprint of Collier and Sharp where they apply our techniques to variab

Scientific paper

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.

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