Automorphic integrals with log-polynomial period functions and arithmetical identities

Building on the works of S. Bochner equivalence modular relation with functional equation associated to Dirichlet series, K. Chandrasekharan and R. Narasimhan obtained new equivalences between some arithmetical identities. Sister Ann M. Heath considered in Hawkins Knopp context showed its two identities entire cusp integrals involving rational period functions for full group. In this paper we use techniques prove results analogous those Heath. Specifically, establish a automorphic log-polynomial-period discrete Hecke groups.