Abstract : In this talk I shall be describing results obtained from a joint research project with Ming-hsuan Kang of Chiao-Tung University, Taiwan, and a conjecture that we have formulated which generalizes the results obtained so far. Suppose that G=SL_2(F) for some non-archimedean local field F, and that Γ is a discrete torsion-free co-compact subgroup of G. Ihara showed how to associate a complex power series called the Ihara zeta function with any such Γ. It can be thought of as revealing combinatorial information about the quotient of the Bruhat-Tits tree of G by the action of Γ, which is a finite graph. Later this was generalized and a notion of Ihara zeta function was formulated for arbitrary finite graphs. In the case just mentioned where G=SL_2(F), it can be shown that there is a relationship between the Ihara zeta function and an alternating product of determinants of twisted Poincaré series for parabolic subgroups of the affine Weyl group of G. We shall describe how this can be generalized to split simple algebraic groups of rank two over F. This will involve formulating a generalization of the Ihara zeta function to finite simplicial complexes of dimension greater than one (the quotients of the Bruhat-Tits building of the groups in question by the action of a discrete subgroup). Then we shall state a conjecture about how this might generalize further to algebraic groups of higher rank. The results obtained for split groups of rank two have been submitted for publication but the conjecture is still open.