On Modular Relations for the Göllnitz-Gordon Functions with Applications to Partitions

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Abstract

In a manuscript of Ramanujan, published with his Lost Notebook [21, pp. 236-237], there are forty identities involving the Rogers-Ramanujan functions. According to G. N. Watson, the beauty of these identities are comparable to that of the Rogers- Ramanujan identities. In the paper, we establish modular relations involving the Göllnitz-Gordon functions which are analogous to Ramanujan's forty identities. Furthermore, we extract interesting partition results from some of the modular relations.

Original languageEnglish
Pages (from-to)178-216
Number of pages39
JournalJournal of Number Theory
Volume68
Issue number2
DOIs
Publication statusPublished - 1998 Feb 1

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All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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