The Ramanujan Journal

, Volume 43, Issue 2, pp 347–357 | Cite as

Congruences related to the Ramanujan/Watson mock theta functions \(\omega (q)\) and \(\nu (q)\)

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


Recently, Andrews, Dixit, and Yee introduced partition functions associated with the Ramanujan/Watson mock theta functions \(\omega (q)\) and \(\nu (q)\). 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 \(\omega (q)\) given by Waldherr is presented.


Partition congruences Generating function Mock theta functions 

Mathematics Subject Classification

Primary 11P81 11P83 



The authors are grateful to the referee for very valuable comments and suggestions.


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • George E. Andrews
    • 1
  • Donny Passary
    • 1
  • James A. Sellers
    • 1
  • Ae Ja Yee
    • 1
  1. 1.Department of MathematicsThe Pennsylvania State UniversityUniversity ParkUSA

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