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

Hannah E. Burson

doi:10.1007/s00026-019-00454-7

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

Hannah E. Burson

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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 language	English (US)
Pages (from-to)	579-588
Number of pages	10
Journal	Annals of Combinatorics
Volume	23
Issue number	3-4
DOIs	https://doi.org/10.1007/s00026-019-00454-7
State	Published - Nov 1 2019
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2019, Springer Nature Switzerland AG.

Keywords

False theta functions
Overpartitions
Partitions

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10.1007/s00026-019-00454-7

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KW - Overpartitions

KW - Partitions

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

Abstract

Bibliographical note

Keywords

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