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

Published online by Cambridge University Press:  22 January 2016

Ramesh Gangolli  and
Garth Warner
Ramesh Gangolli
Affiliation:
Department of MathematicsUniversity of WashingtonSeattle, Washington 98195
Garth Warner
Affiliation:
Department of MathematicsUniversity of WashingtonSeattle, Washington 98195
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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 ZΓ of Selberg’s type attached to the data (G, K, Γ).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 78 , May 1980 , pp. 1 - 44
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1980

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