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.