On Rogers–Ramanujan functions, binary quadratic forms and eta-quotients
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- by Alexander Berkovich and Hamza Yesilyurt PDF
- Proc. Amer. Math. Soc. 142 (2014), 777-793 Request permission
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.References
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Additional Information
- Alexander Berkovich
- Affiliation: Department of Mathematics, University of Florida, 358 Little Hall, Gainesville, Florida 32611
- MR Author ID: 247760
- Email: alexb@ufl.edu
- Hamza Yesilyurt
- Affiliation: Department of Mathematics, Bilkent University, 06800 Bilkent, Ankara, Turkey
- Email: hamza@fen.bilkent.edu.tr
- Received by editor(s): April 7, 2012
- Published electronically: December 2, 2013
- Additional Notes: The first author’s research was partially supported by grant H98230-09-1-0051 of the National Security Agency
The second author’s research was partially supported by grant 109T669 from Tübitak - Communicated by: Ken Ono
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 142 (2014), 777-793
- MSC (2010): Primary 11E16, 11E45, 11F03, 11P84
- DOI: https://doi.org/10.1090/S0002-9939-2013-11816-2
- MathSciNet review: 3148513