Partitions associated with the Ramanujan/Watson mock theta functions ω(q), ν(q)and ϕ(q)

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Abstract

The generating function of partitions with repeated (resp. distinct) parts such that each odd part is less than twice the smallest part is shown to be the third order mock theta function ω(q) (resp. ν(−q)). Similar results for partitions with the corresponding restriction on each even part are also obtained, one of which involves the third order mock theta function ϕ(q). Congruences for the smallest parts partition function(s) associated to such partitions are obtained. Two analogues of the partition-theoretic interpretation of Euler’s pentagonal number theorem are also obtained.

Original languageEnglish (US)
Article number19
JournalResearch in Number Theory
Volume1
Issue number1
DOIs
StatePublished - Dec 1 2015

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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