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 PSL(2,R), generalizing earlier work of Sarnak and Bourgain-Kontorovich 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.