%0 Journal Article %T A relation of cusp forms and Maass forms on product of hyperbolic Riemann orbisurfaces of finite volume %A Anilatmaja Aryasomayajula %J Mathematics %D 2014 %I arXiv %X In 2006, in a paper published in Compositio, titled "Bounds on canonical Green's functions", J. Jorgenson and J. Kramer proved a certain key identity which relates the two natural metrics, namely the hyperbolic metric and the canonical metric defined on a compact hyperbolic Riemann surface. In this article, we extend this identity to product of noncompact hyperbolic Riemann orbisurfaces of finite volume, which can be realized as a quotient space of the action of a Fuchsian subgroup of first kind on the hyperbolic upper half plane. %U http://arxiv.org/abs/1401.7126v1