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

Krishnaswami Alladi, George E. Andrews, Alexander Berkovich

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


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
Issue number2
StatePublished - 2003

All Science Journal Classification (ASJC) codes

  • Mathematics(all)


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