On Rogers-Ramanujan functions, binary quadratic forms and eta-quotients

Details On Rogers-Ramanujan functions, binary quadratic forms and eta-quotients On Rogers-Ramanujan functions, binary quadratic forms and eta-quotients

2012-04-04

arxiv.org/abs/1204.1092v2

Mathematics

Number Theory

14 pages, no figures, no typos

Scientific paper

In a handwritten manuscript published with his lost notebook, Ramanujan stated without proofs forty identities for the Rogers-Ramanujan functions. We observe that the functions that appear in Ramanujan's identities can be obtained from a Hecke action on a certain family of eta products. We establish further Hecke-type relations for these functions involving binary quadratic forms. Our observations enable us to find new identities for the Rogers-Ramanujan functions and also to use such identities in turn to find identities involving binary quadratic forms.

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