Gamma factors and Plancherel measures
Gamma factors and Plancherel measures
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伽玛因子和 Plancherel 测量
DOI：
10.3792/pjaa.68.256
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发表时间：
1992
期刊：
影响因子：
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通讯作者：
N. Kurokawa
中科院分区：
文献类型：
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作者：
N. Kurokawa
我们显式地计算了Selberg - zeta函数的gamma因子，并给出了相关Plancherel测度的简洁公式。这份报告补充了前一份报告。细节在[8]中有描述，将在其他地方发布。1. 塞尔伯格函数。我们修正了Selberg zeta函数的符号，主要包括Selberg[13]、Gangolli[5]、Fried [4] （x 1）和Wakayama[15]。设M F\ G/K是秩为1的紧局部对称空间。我们用ZM(S)表示Selberg ζ函数：Z(S) II II (1n (p)-S-a) Prim(M) 0，其中Prim(M)是M的素数测线集合，其范数函数N (p) exp（长度(p)）和/2在某个半格上运行。我们回顾了以下事实：Zt(s)作为dim M阶的亚纯函数对所有s C有解析延拓，并有如下的泛函方程
We explicitly calculate gamma factors of Selberg zeta functions and give a neat formula to the associated Plancherel measures. This report supplements the previous one [7]. The details are described in [8] and will be published elsewhere. 1. Selberg zeta functions. We fix the notation for Selberg zeta functions following mainly Selberg[13], Gangolli [5], Fried [4] (x 1), and Wakayama [15]. Let M F\ G/K be a compact locally symmetric space of rank one. We denote by ZM(S) the Selberg zeta function: Z(s) II II (1 N (p)-S-a) PPrim(M) 0 where Prim(M) is the set of prime geodesics of M with the norm function N (p) exp(length(p)) and /2 runs over a certain semi-lattice. We recall the following fact: Zt(s) has an analytic continuation to all s C as a meromorphic function of order dim M and has the following functional equation