Selberg zeta functions and Ruelle operators for function fields (Q1185138)

Let \(\mathbb{F}\) be a finite field with \(q\) elements where \(q\) is odd. The group \(\Gamma=PGL(2,\mathbb{F}[T])\) has many properties in common with \(PSL(2,\mathbb{Z})\). In particular, there is a zeta function of Selberg's type associated with \(\Gamma\). This function was explicitly determined by Akagawa. The author gives a new short approach to Akagawa's result which is based on the discussion of the determinant of the identity minus the Ruelle operator.