On the Modulus of the Selberg Zeta-Functions in the Critical Strip

Abstract

We investigate the behavior of the real part of the logarithmic derivatives of the Selberg zeta-functions ZPSL(2,Z)(s) and ZC (s) in the critical strip 0 < σ < 1. The functions ZPSL(2,Z)(s) and ZC (s) are defined on the modular group and on the compact Riemann surface, respectively.

Keywords

• Selberg zeta-function
• modular group
• compact Riemann surface
• Riemann zeta-function
• critical strip