Effective congruences for mock theta functions
Summary: Let \(M(q)=\sum c(n)q^n\) be one of Ramanujan's mock theta functions. We establish the existence of infinitely many linear congruences of the form: \[ c(An+B)\equiv 0\pmod{\ell^j} \] where A is a multiple of \(\ell\) and an auxiliary prime, \(p\). Moreover, we give an effectively computable upper bound on the smallest such \(p\) for which these congruences hold. The effective nature of our results is based on the prior works of \textit{S. Lichtenstein} [Proc. Am. Math. Soc. 136, No. 10, 3419--3428 (2008; Zbl 1247.11069)] and \textit{S. Treneer} [ibid. (3) 93, No. 2, 304--324 (2006; Zbl 1165.11316)].
scientific article; zbMATH DE number 6334779
scientific article