## Advanced Studies in Pure Mathematics

### Zeta Functions of Loop Groups

Shin-ya Koyama

#### Abstract

We will make a preparation for defining the Selberg zeta function of $PSL(2, \mathbf{Z}[T])$, which is a discrete subgroup of the loop group $G$ of $PSL(2, \mathbf{C})$. Conjugacy classes of $PSL(2, \mathbf{Z}[T])$ will be classified and the definition of the norm of hyperbolic classes will be proposed.

#### Article information

Dates
First available in Project Euclid: 15 August 2018

https://projecteuclid.org/ euclid.aspm/1534359130

Digital Object Identifier
doi:10.2969/aspm/02110227

Mathematical Reviews number (MathSciNet)
MR1210792

Zentralblatt MATH identifier
0807.11041

#### Citation

Koyama, Shin-ya. Zeta Functions of Loop Groups. Zeta Functions in Geometry, 227--235, Mathematical Society of Japan, Tokyo, Japan, 1992. doi:10.2969/aspm/02110227. https://projecteuclid.org/euclid.aspm/1534359130