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
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The authors are grateful to the referee for very valuable comments and suggestions.
Andrews, G.E., Dixit, A., Yee, A.J.: Partitions associated with the Ramanujan/Watson mock theta functions \(\omega (q), \nu (q)\) and \(\phi (q)\). Res. Number Theory 1, 19 (2015)MathSciNetCrossRefMATHGoogle Scholar