Congruences related to the Ramanujan/Watson mock theta functions ω(q) and ν(q)

George E. Andrews; Donny Passary; James A. Sellers; Ae Ja Yee

doi:10.1007/s11139-016-9812-2

Congruences related to the Ramanujan/Watson mock theta functions ω(q) and ν(q)

George E. Andrews, Donny Passary, James A. Sellers, Ae Ja Yee

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29 Scopus citations

Abstract

Recently, Andrews, Dixit, and Yee introduced partition functions associated with the Ramanujan/Watson mock theta functions ω(q) and ν(q). In this paper, we study arithmetic properties of the partition functions. Based on one of the results of Andrews, Dixit, and Yee, mod 2 congruences are obtained. In addition, infinite families of mod 4 and mod 8 congruences are presented. Lastly, an elementary proof of the first explicit examples of congruences for ω(q) given by Waldherr is presented.

Original language	English (US)
Pages (from-to)	347-357
Number of pages	11
Journal	Ramanujan Journal
Volume	43
Issue number	2
DOIs	https://doi.org/10.1007/s11139-016-9812-2
State	Published - Jun 1 2017
Externally published	Yes

Bibliographical note

Funding Information:
The fourth author was partially supported by a grant () from the Simons Foundation.

Publisher Copyright:
© 2016, Springer Science+Business Media New York.

Keywords

Generating function
Mock theta functions
Partition congruences

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AU - Passary, Donny

AU - Sellers, James A.

AU - Yee, Ae Ja

PY - 2017/6/1

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Congruences related to the Ramanujan/Watson mock theta functions ω(q) and ν(q)

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