A new four parameter q-series identity and its partition implications

Krishnaswami Alladi, George E. Andrews, Alexander Berkovich

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

We prove a new four parameter q-hypergeometric series identity from which the three parameter identity for the Göllnitz theorem due to Alladi, Andrews, and Gordon follows as a special case by setting one of the parameters equal to 0. The new identity is equivalent to a four parameter partition theorem which extends the deep theorem of Göllnitz and thereby settles a problem raised by Andrews thirty years ago. Some consequences including a quadruple product extension of Jacobi's triple product identity, and prospects of future research are briefly discussed.

Original languageEnglish (US)
Pages (from-to)231-260
Number of pages30
JournalInventiones Mathematicae
Volume153
Issue number2
DOIs
StatePublished - Aug 11 2003

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Q-series
Partition
Jacobi's Triple Product Identity
Theorem
Hypergeometric Series
Quadruple

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Alladi, Krishnaswami ; Andrews, George E. ; Berkovich, Alexander. / A new four parameter q-series identity and its partition implications. In: Inventiones Mathematicae. 2003 ; Vol. 153, No. 2. pp. 231-260.
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A new four parameter q-series identity and its partition implications. / Alladi, Krishnaswami; Andrews, George E.; Berkovich, Alexander.

In: Inventiones Mathematicae, Vol. 153, No. 2, 11.08.2003, p. 231-260.

Research output: Contribution to journalArticle

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