Proofs of conjectures of Sandon and Zanello on colored partition identities

Bruce C. Berndt, Roberta R. Zhou

Research output: Contribution to journalArticlepeer-review

Abstract

In a recent systematic study, C. Sandon and F. Zanello of- fered 30 conjectured identities for partitions. As a consequence of their study of partition identities arising from Ramanujan's formulas for mul- tipliers in the theory of modular equations, the present authors in an earlier paper proved three of these conjectures. In this paper, we provide proofs for the remaining 27 conjectures of Sandon and Zanello. Most of our proofs depend upon known modular equations and formulas of Ra- manujan for theta functions, while for the remainder of our proofs it was necessary to derive new modular equations and to employ the process of duplication to extend Ramanujan's catalogue of theta function formulas.

Original languageEnglish (US)
Pages (from-to)987-1028
Number of pages42
JournalJournal of the Korean Mathematical Society
Volume51
Issue number5
DOIs
StatePublished - 2014
Externally publishedYes

Keywords

  • Colored partitions
  • Modular equations
  • Theta function identities

ASJC Scopus subject areas

  • General Mathematics

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