Huber's theorem for hyperbolic orbisurfaces by Emily B. Dryden and Alexander Strohmaier (2005, revised 2007)

Author preprint: arxiv.org/abs/math/0504571v2

Full text: arxiv.org/pdf/math/0504571

Section 1 states the compact orientable setting and oriented closed-geodesic multiplicities. Section 2, equation (1), page 3, gives the Selberg trace formula with its spectral normalization; the following discussion identifies primitive oriented geodesics and iterates.