Distribution and divisibility of the Fourier coefficients of certain Hauptmoduln (Q2696069)

The author of the paper under review considers some arithmetic properties of \(j_6(\tau)\) and \(j_{10}(\tau)\), that is, Hauptmoduln of the congruence subgroup \(\Gamma_0(N)\) and \(j_6^*(\tau)\) and \(j_{10}^*(\tau)\), that is, Hauptmoduln of the Fricke group \(\Gamma_0(N)\). These are arithmetically rich objects since they can be expressed in terms of the Dedekind-eta quotients. As a main result, he finds some arithmetic progression of Fourier coefficients of those. As an application the author finds infinite families of congruences for those Hauptmodlns. Hecke eigenforms and Rogers-Ramanujan continued fraction are the main ingredients for this result.