  In 2006, in a paper published in Compositio titled "Bounds on canonical
Green's functions", J. Jorgenson and J. Kramer derived bounds for the canonical
Green's function and the hyperbolic Green's function defined on a compact
hyperbolic Riemann surface. In this article, we extend these bounds to
noncompact hyperbolic Riemann orbisurfaces of finite volume and of genus
greater than zero, which can be realized as a quotient space of the action of a
Fuchsian subgroup of first kind on the hyperbolic upper half-plane.
  Our bounds are optimally derived by following the methods from the above
mentioned paper of J. Jorgenson and J. Kramer.

Number Theory