Zeta functions of Selberg’s type for some noncompact quotients of symmetric spaces of rank one

Ramesh Gangolli, Garth Warner

Type: Article

Publication Date: 1980-05-01

Citations: 106

DOI: https://doi.org/10.1017/s002776300001878x

Abstract

In a previous paper [5], one of the present authors has worked out a theory of zeta functions of Selberg’s type for compact quotients of symmetric spaces of rank one. In the present paper, we consider the analogues of those results when G/K is a noncompact symmetric space of rank one and Γ is a discrete subgroup of G such that G/Γ is not compact but such that vol( G/Γ )<∞. Thus, Γ is a non-uniform lattice. Certain mild restrictions, which are fulfilled in many arithmetic cases, will be put on Γ , and we shall consider how one can define a zeta function Z Γ of Selberg’s type attached to the data ( G, K, Γ ).

Locations

Nagoya Mathematical Journal - View - PDF
Project Euclid (Cornell University) - View - PDF

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