Abstract
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.
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The authors are grateful to the referee for very valuable comments and suggestions.
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The fourth author was partially supported by a grant (\(\#280903\)) from the Simons Foundation.
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Andrews, G.E., Passary, D., Sellers, J.A. et al. Congruences related to the Ramanujan/Watson mock theta functions \(\omega (q)\) and \(\nu (q)\) . Ramanujan J 43, 347–357 (2017). https://doi.org/10.1007/s11139-016-9812-2
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DOI: https://doi.org/10.1007/s11139-016-9812-2