Some basic questions about the Selberg zeta function I'm trying to learn about the Selberg zeta function, but it seems like introductory texts assume more knowledge of Riemannian geometry than I'm comfortable with.
I have some basic questions that someone might be able to help with:
Is the composition of two closed geodesics itself a closed geodesic?
Is composition of geodesics a commutative operation?
Can all geodesics be decomposed into compositions of primitive closed geodesics?
If anyone has comments or references, I would appreciate them.

http://arxiv.org/abs/math/0407288 you may start your voyage here with 'introduction to the Selberg zeta function' it explain its role for Riemann Hypothesis and a generalization of the Poisson summation formula
http://matwbn.icm.edu.pl/ksiazki/aa/aa91/aa9132.pdf HERE it explain the Zeta function of Selberg in term of the determinant of a certain Laplacian over the surface , also the zeta regularization for determinant is used
for zeta regularization and functional determinants see http://arxiv.org/PS_cache/arxiv/pdf/1108/1108.5659v1.pdf
