On Rogers-Ramanujan functions, binary quadratic froms and eta-quotients
Date
2014Source Title
Proceedings of the American Mathematical Society
Print ISSN
0002-9939
Electronic ISSN
1088-6834
Publisher
American Mathematical Society
Volume
142
Issue
3
Pages
777 - 793
Language
English
Type
ArticleItem Usage Stats
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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 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. © 2013 American Mathematical Society.
Keywords
Binary Quadratic FormsEta-quotients
Ramanujan's Lost Notebook
Rogers-ramanujan Functions
Thompson Series