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

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      Author(s)
      Berkovich, A.
      Yeşilyurt, H.
      Date
      2014
      Source 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
      Article
      Item 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 Forms
      Eta-quotients
      Ramanujan's Lost Notebook
      Rogers-ramanujan Functions
      Thompson Series
      Permalink
      http://hdl.handle.net/11693/13147
      Published Version (Please cite this version)
      http://dx.doi.org/10.1090/S0002-9939-2013-11816-2
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      • Department of Mathematics 653
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