A reciprocity theorem for certain q-series found in Ramanujan's lost notebook

Bruce C. Berndt, Song Heng Chan, Boon Pin Yeap, Ae Ja Yee

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

Three proofs are given for a reciprocity theorem for a certain q-series found in Ramanujan's lost notebook. The first proof uses Ramanujan's 1 ψ 1 summation theorem, the second employs an identity of N. J. Fine, and the third is combinatorial. Next, we show that the reciprocity theorem leads to a two variable generalization of the quintuple product identity. The paper concludes with an application to sums of three squares.

Original languageEnglish (US)
Pages (from-to)27-37
Number of pages11
JournalRamanujan Journal
Volume13
Issue number1-3
DOIs
StatePublished - Jun 1 2007

Fingerprint

Ramanujan's Lost Notebook
Q-series
Reciprocity
Theorem
Ramanujan
Summation

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Cite this

Berndt, Bruce C. ; Chan, Song Heng ; Yeap, Boon Pin ; Yee, Ae Ja. / A reciprocity theorem for certain q-series found in Ramanujan's lost notebook. In: Ramanujan Journal. 2007 ; Vol. 13, No. 1-3. pp. 27-37.
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A reciprocity theorem for certain q-series found in Ramanujan's lost notebook. / Berndt, Bruce C.; Chan, Song Heng; Yeap, Boon Pin; Yee, Ae Ja.

In: Ramanujan Journal, Vol. 13, No. 1-3, 01.06.2007, p. 27-37.

Research output: Contribution to journalArticle

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