  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.

Number Theory