Abstract
Let Z(s) be the Selberg zeta-function associated to a compact Riemann surface. We consider decompositions Z(s) = f(h(s)), where f and h are meromorphic functions, and show that such decompositions can only be trivial.
Highlights
We continue the investigation of decompositions of the Selberg zeta-function which was started in Garunkstis and Steuding [6]
The Selberg zeta-function Z associated with a compact Riemann surface of genus g is pseudo-prime and right-prime
The Selberg zeta-function Z associated with a compact Riemann surface of genus g ≥ 2 is prime
Summary
We continue the investigation of decompositions of the Selberg zeta-function which was started in Garunkstis and Steuding [6]. Defines the Selberg zeta-function in the half-plane σ > 1. The Selberg zeta-function Z associated with a compact Riemann surface of genus g is pseudo-prime and right-prime.
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