Zeta functions of Selberg’s type for some noncompact quotients of symmetric spaces of rank one
Zeta functions of Selberg’s type for some noncompact quotients of symmetric spaces of rank one
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对于一阶对称空间的一些非紧商，Selberg 型 Zeta 函数
DOI：
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发表时间：
1980
影响因子：
0.8
通讯作者：
Garth Warner
中科院分区：
文献类型：
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作者：
R. Gangolli;Garth Warner
本文作者之一曾在文献[5]中对秩为1的对称空间的紧导数给出了Selberg型zeta函数的理论。当G/K是秩为1的非紧对称空间，且Γ是G的离散子群，使得G/Γ不是紧的，但使得vol（G/Γ）<∞时，本文考虑了上述结果的类似结果.因此，r是非均匀晶格。某些在许多算术情况下都能满足的温和限制将加在Γ上，我们将考虑如何定义一个与数据（G，K，Γ）有关的塞尔伯格型ζ函数ZΓ。
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).