### 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 language | English (US) |
---|---|

Article number | 19 |

Journal | Research in Number Theory |

Volume | 1 |

Issue number | 1 |

DOIs | |

State | Published - Dec 1 2015 |

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### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory

### Cite this

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**Partitions associated with the Ramanujan/Watson mock theta functions ω(q), ν(q)and ϕ(q).** / Andrews, George E.; Dixit, Atul; Yee, Ae Ja.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Partitions associated with the Ramanujan/Watson mock theta functions ω(q), ν(q)and ϕ(q)

AU - Andrews, George E.

AU - Dixit, Atul

AU - Yee, Ae Ja

PY - 2015/12/1

Y1 - 2015/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85006624407&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85006624407&partnerID=8YFLogxK

U2 - 10.1007/s40993-015-0020-8

DO - 10.1007/s40993-015-0020-8

M3 - Article

AN - SCOPUS:85006624407

VL - 1

JO - Research in Number Theory

JF - Research in Number Theory

SN - 2363-9555

IS - 1

M1 - 19

ER -