Counting and Equidistribution of Reciprocal Geodesics and Dihedral Groups

Abstract We study the growth of the number of conjugacy classes of infinite dihedral subgroups of lattices in PSL₂R, generalizing the earlier work of Sarnak 9 and Bourgain–Kontorovich 4 on the growth of the number of reciprocal geodesics on the modular surface. We also prove that reciprocal geodesics are equidistributed in the unit tangent bundle.