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We study the growth of the number of conjugacy classes of infinite dihedralsubgroups of lattices in PSL(2,R), generalizing earlier work of Sarnak andBourgain-Kontorovich on the growth of the number of reciprocal geodesics on themodular surface. We also prove that reciprocal geodesics are equidistributed inthe unit tangent bundle.

Counting and equidistribution of reciprocal geodesics and dihedral groups