An algorithmic approach to Ramanujan-Kolberg identities

Let M be a given positive integer and r = (rδ)δ|M a sequence indexed by the positive divisors δ of M . In this paper we present an algorithm that takes as input a generating function of the form ∑∞ n=0 ar(n)q n := ∏ δ|M ∏∞ n=1(1−q )δ and positive integers m, N and t ∈ {0, . . . ,m−1}. Given this data we compute a set Pm,r(t) which contains t and is uniquely defined by m, r and t. Next we decide if there exists a sequence (sδ)δ|N indexed by the positive divisors δ of N , and modular functions b1, . . . , bk on Γ0(N) (where each bj equals the product of finitely many terms from {q ∏∞ n=1(1− q ) : δ|N}), such that: q α ∏