Zeta functions of adjacency algebras of association schemes of prime order or rank two

For a module L which has only finitely many submodules with a given finite index we define the zeta function of L to be a formal Dirichlet series zeta(L) (s) = Sigma(n >= 1) a(n)n(-s) where a(n) is the number of submodules of L with index n. For a commutative ring R and an association scheme (X, S) we denote the adjacency algebra of (X, S) over R by RS. In this article we aim to compute zeta(ZS)(s), where ZS is viewed as a regular ZS-module, under the assumption that vertical bar X vertical bar is a prime or vertical bar S vertical bar = 2.ArticleHOKKAIDO MATHEMATICAL JOURNAL. 45(1):75-91 (2016)journal articl