This thesis studies the fundamental automorphic function theory associated to a markedgenus zero curve over a finite field. Following insights from topological field theory, one expects this theory is deeply related to the unramified automorphic representation theory of general function fields. There are two main contributions. First I present an explicit description of the action of Hecke operators for the groups PGL2 and SL3. Second, I give a conjecture, along with some evidence, that characterizes the action of Hecke operators on Eisenstein series for any group.