Selberg Zeta Function
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High Quality Content by WIKIPEDIA articles! The Selberg zeta-function was introduced by Atle Selberg (1956). It is analogous to the famous Riemann zeta function zeta(s) = prod_{pinmathbb{P}} frac{1}{1-p^{-s}} where mathbb{P} is the set of prime numbers. The Selberg zeta-function uses the lengths of simple closed geodesics instead of the primes numbers. For any hyperbolic surface of finite area there is an associated Selberg zeta-function; this function is a meromorphic function defined in the complex plane. The zeta function is defined in terms of the closed geodesics of the surface. The zeros...
High Quality Content by WIKIPEDIA articles! The Selberg zeta-function was introduced by Atle Selberg (1956). It is analogous to the famous Riemann zeta function zeta(s) = prod_{pinmathbb{P}} frac{1}{1-p^{-s}} where mathbb{P} is the set of prime numbers. The Selberg zeta-function uses the lengths of simple closed geodesics instead of the primes numbers. For any hyperbolic surface of finite area there is an associated Selberg zeta-function; this function is a meromorphic function defined in the complex plane. The zeta function is defined in terms of the closed geodesics of the surface. The zeros and poles of the Selberg zeta-function, Z(s), can be described in terms of spectral data of the surface.
