A Bijective Proof of a False Theta Function Identity from Ramanujan’s Lost Notebook

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Abstract

In his lost notebook, Ramanujan listed five identities related to the false theta function: f(q)=∑n=0∞(-1)nqn(n+1)/2.A new combinatorial interpretation and a proof of one of these identities are given. The methods of the proof allow for new multivariate generalizations of this identity. Additionally, the same technique can be used to obtain a combinatorial interpretation of another one of the identities.

Original languageEnglish (US)
Pages (from-to)579-588
Number of pages10
JournalAnnals of Combinatorics
Volume23
Issue number3-4
DOIs
StatePublished - Nov 1 2019
Externally publishedYes

Keywords

  • False theta functions
  • Overpartitions
  • Partitions

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