Mitsugu Hirasaka, Zeta functions of adjacecny algebras

For a module L the formal Dirichlet series $\zeta$_L(s) = ∑_{n ≥ 1</i>}a_nn^-s is defined whenever the number a_n of submodules of L with index n is finite for each positive integer n. For a ring R and a finite association scheme (X,S) we denote the adjacency algebra of (X,S) over R by RS. In this talk we aim to compute $\zeta$_ZS(s) where $$ZS is regarded as a $$ZS-module under the assumption that $|X|$ is prime or $|S|=2$.</p>