Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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PROOFS OF CONJECTURES OF SANDON AND ZANELLO ON COLORED PARTITION IDENTITIES

  • Berndt, Bruce C. (Department of Mathematics University of Illinois) ;
  • Zhou, Roberta R. (School of Mathematics and Statistics Northeastern University at Qinhuangdao, School of Mathematical Sciences Dalian University of Technology)
  • Received : 2013.10.14
  • Published : 2014.09.01
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Abstract

In a recent systematic study, C. Sandon and F. Zanello offered 30 conjectured identities for partitions. As a consequence of their study of partition identities arising from Ramanujan's formulas for multipliers 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 Ramanujan 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.

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References

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