A relation of cusp forms and Maass forms on product of hyperbolic Riemann orbisurfaces of finite volume

2014/01/28 by Anilatmaja Aryasomayajula, Aryasomayajula, Anilatmaja
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1401.7126

openalex publication_date 2014/01/28 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

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.

Related

• Extension of a key identity
• Bounds for Green's functions on noncompact hyperbolic Riemann\n orbisurfaces of finite volume
• Bounds for canonical Green's function at cusps
• Estimates of Kähler metrics on noncompact finite volume hyperbolic Riemann surfaces, and their symmetric products
• Cusps and the family hyperbolic metric