Rogers–Ramanujan type generalized reciprocal identities and Eisenstein series

In a recent paper Huber and Schultz have given relations between eta quotients and Rogers–Ramanujan type generalized reciprocal identities. Inspired by that work, we study the relationship between the Eisenstein series and the level p generalized reciprocal identities, where p is a prime that is congruent to 1 modulo 4, by employing techniques from modular forms. In the aforementioned paper, Huber and Schultz additionally point to a relationship between these reciprocals and the class number of the field ℚ(√(p)) . Our methods allow us to give this relationship explicitly by obtaining a formula for the class number of the field ℚ(√(p)) which involves Fourier coefficients of these reciprocals.