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Ramanujan’s ‘‘Lost Notebook’’ and the Virasoro Algebra

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Abstract

By using the theory of vertex operator algebras, we gave a new proof of the famous Ramanujan’s modulus 5 modular equation from his ‘‘Lost Notebook’’ (p. 139 in [R]). Furthermore, we obtained an infinite list of q-identities for all odd moduli; thus, we generalized the result of Ramanujan.

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Author notes

  1. A. Milas

    Present address: Department of Mathematics, University at Albany (SUNY), 1400 Washington Road, Albany, NY, 12222, USA

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  1. Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY, 12180, USA

    A. Milas

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  1. A. Milas
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Correspondence to A. Milas.

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Communicated by L. Takhtajan

Acknowledgements It was indeed hard to trace all the known proofs of (1.1), (1.2) and (1.3). We apologize if some important references are omitted. We would like to thank Jim Lepowsky for conversations on many related subjects. A few years ago Lepowsky and the author were trying to relate classical Rogers-Ramanujan identities and Zhu’s work [Z]. We also thank Bruce Berndt for pointing us to [BrO] and Steve Milne for bringing [Mi] to our attention.

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Milas, A. Ramanujan’s ‘‘Lost Notebook’’ and the Virasoro Algebra. Commun. Math. Phys. 251, 567–588 (2004). https://doi.org/10.1007/s00220-004-1179-3

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