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arXiv · 1204.1092

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

Alexander Berkovich·Hamza Yesilyurt
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Abstract

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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Alexander Berkovich, Hamza Yesilyurt. 2012-04-04. On Rogers-Ramanujan functions, binary quadratic forms and eta-quotients. https://arxiv.org/abs/1204.1092

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