On Rogers–Ramanujan functions, binary quadratic forms and eta-quotients
Author:
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 function that appears 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 return to find identities involving binary quadratic forms.
Publisher
American Mathematical Society (AMS)
Subject
Applied Mathematics,General Mathematics
Link
http://www.ams.org/proc/2014-142-03/S0002-9939-2013-11816-2/S0002-9939-2013-11816-2.pdf
Reference15 articles.
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4. Ramanujan’s forty identities for the Rogers-Ramanujan functions;Berndt, Bruce C.;Mem. Amer. Math. Soc.,2007
5. A proof of some identities of Ramanujan using modular forms;Biagioli, Anthony J. F.;Glasgow Math. J.,1989
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1. Automatic Proof of Theta-Function Identities;Texts & Monographs in Symbolic Computation;2019
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