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

doi:10.1007/s11139-006-0241-5

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

Mathematics

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

19 Scopus citations

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 ₁ψ₁ 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 language	English (US)
Pages (from-to)	27-37
Number of pages	11
Journal	Ramanujan Journal
Volume	13
Issue number	1-3
DOIs	https://doi.org/10.1007/s11139-006-0241-5
State	Published - Jun 2007

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1007/s11139-006-0241-5

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title = "A reciprocity theorem for certain q-series found in Ramanujan's lost notebook",

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 1ψ1 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.",

author = "Berndt, {Bruce C.} and Chan, {Song Heng} and Yeap, {Boon Pin} and Yee, {Ae Ja}",

note = "Funding Information: A. J. Yee: Research partially supported by a grant from The Number Theory Foundation. Funding Information: B. C. Berndt: Research partially supported by grant MDA904-00-1-0015 from the National Security Agency.",

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AU - Yee, Ae Ja

N1 - Funding Information: A. J. Yee: Research partially supported by a grant from The Number Theory Foundation. Funding Information: B. C. Berndt: Research partially supported by grant MDA904-00-1-0015 from the National Security Agency.

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N2 - 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 1ψ1 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.

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

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