Partitions associated with three third order mock theta functions

Ae Ja Yee (이애자)

Department of Mathematics, The Pennsylvania State University, University Park, PA, USA

Department of Mathematics, The Pennsylvania State University, University Park, PA, USA

2015/06/23 Tue 4PM-5PM

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 functions associated to such partitions are obtained. Two analogues of the partition-theoretic interpretation of Euler’s pentagonal theorem are also obtained. This is joint work with George Andrews and Atul Dixit.

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