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Let be a finite-volume quotient of the upper-half space, where is a discrete subgroup. To a finite dimensional unitary representation of one associates the Selberg zeta function . In this paper we prove the Artin formalism for the Selberg zeta function. Namely, if is a finite index group extension of in , and is the induced representation, then . In the second part of the paper we prove by a direct method the analogous identity for the scattering function, namely , for an appropriate...
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