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We characterize Maass cusp forms for any cofinite Hecke triangle group as1-eigenfunctions of appropriate regularity of a transfer operator family. Thistransfer operator family is associated to a certain symbolic dynamics for thegeodesic flow on the orbifold arising as the orbit space of the action of theHecke triangle group on the hyperbolic plane. Moreover we show that the Selbergzeta function is the Fredholm determinant of the transfer operator familyassociated to an acceleration of this symbolic dynamics.

Period functions for Hecke triangle groups, and the Selberg zeta function as a Fredholm determinant