2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60674We show that the number of twisted conjugacy classes is infinite for any automorphism of non-elementary, Gromov hyperbolic group . An analog of Selberg theory for twisted conjugacy classes is proposed.10 pages, LatexGroup TheoryAlgebraic TopologyDifferential Geometry20F32, 55M20, 58F20Reidemeister number of any automorphism of a Gromov hyperbolic group is infinitetext