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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 ζL(s) = P n≥1 ann −s where an 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 ζZS(s), where ZS is viewed as a regular ZS-module, under the assumption that |X| is a prime or |S| = 2.

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