Alexander Berkovich, Hamza Yesilyurt
Published 2012-04-04, updated 2012-07-22Version 3
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.
Comments: 14 pages, no figures, no typos. To appear in Proceedings of the AMS
Binary Quadratic forms and the Fourier coefficients of certain weight 1 eta-quotients
Values of binary quadratic forms at integer points and Schmidt games
On the $Γ$-equivalence of binary quadratic forms
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