[Abstract] Dandan Chen, Rong Chen and Frank Garvan Congruences modulo powers of $5$ and $7$ for the crank and rank parity functions and related mock theta functions , preprint.
Abstract:

Recently we proved congruences modulo powers of $5$ for the rank parity function, and here we extend these congruences for powers of $7$. We also show how these congruences imply congruences modulo powers of $5$ and $7$ for the coefficients of the related third order mock theta function $\omega(q)$, using Atkin-Lehner involutions and transformation results of Zwegers. Finally we a prove a family of congruences modulo powers of $7$ for the crank parity function.

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Created by F.G. Garvan (fgarvan@ufl.edu) on Wednesday, July 10, 2024.
Last update made Wed Jul 10 20:38:30 CDT 2024.

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