The smallest parts function associated with $\omega (q)$

Abstract

We establish two families of congruences modulo powers of 5 for the Fourier coefficients of $(2E_2(2\tau )-E_2(\tau ))\eta (2\tau {)}^{-1}$, where $E_2(\tau )$ is the weight 2 Eisenstein series and $\eta (\tau )$ is the Dedekind eta function. This allows us to prove similar congruences for two smallest parts functions. The first function is ${\mathrm{spt}}_{\omega }(n)$, which was introduced by Andrews, Dixit and Yee and associated with Ramanujan/Watson's third order mock theta function $\omega (q)$. The second one is ${\mathrm{spt}}_{C5}(n)$, which appeared in the work of Garvan and Jennings-Shaffer. Moreover, we confirm two conjectural congruences of Wang.

17 pages

References in corpus (1)

• Exotic Bailey-Slater SPT-Functions II: Hecke-Rogers-Type Double Sums and Bailey Pairs From Groups A, C, E