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Article overview
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The smallest parts function associated with $omega(q)$ | | Liuquan Wang
; Yifan Yang
; | | Date: |
2 Dec 2018 | | Abstract: | We establish two families of congruences modulo powers of 5 for the Fourier
coefficients of $(2E_2(2 au)-E_2( au))eta(2 au)^{-1}$, where $E_2( au)$ is
the weight 2 Eisenstein series and $eta( au)$ 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. | | Source: | arXiv, 1812.0379 | | Services: | Forum | Review | PDF | Favorites | |
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