  In 1961, Chandrasekharan and Narasimhan showed that for a large class of
Dirichlet series the functional equation and two types of arithmetical
identities are equivalent. In 1992, Hawkins and Knopp proved a Hecke
correspondence theorem for modular integrals with rational period function on
theta group. Analogous to Chandrasekharan and Narasimhan, in 2015 Sister Ann M.
Heath has shown that the functional equation in Hawkins and Knopp context and
two type of arithmetical identities are equivalent. She considered the
functional equation and showed its equivalence to two arithmetical identities
associated with entire modular cusp integrals involving rational period
functions for the full modular group. In this paper we extend the results of
Sister Ann M. Heath to entire automorphic integrals involving rational period
functions on discrete Hecke group.
