The smallest parts function associated with omega(q)
Journal
INTERNATIONAL JOURNAL OF NUMBER THEORY
Journal Volume
18
Journal Issue
10
Pages
2279
Date Issued
2022-11-01
Author(s)
Wang, LQ
Abstract
We establish two families of congruences modulo powers of 5 for the Fourier coefficients of (2E2(2τ) - E2(τ))η(2τ)-1, where E2(τ) is the weight 2 Eisenstein series and η(τ) is the Dedekind eta function. This allows us to prove similar congruences for two smallest parts functions. The first function is sptω(n), which was introduced by Andrews, Dixit and Yee and is associated with Ramanujan/Watson's third-order mock theta function ω(q). The second one is sptC5(n), which appeared in the work of Garvan and Jennings-Shaffer. Moreover, we confirm two conjectural congruences of Wang.
Subjects
Partitions; mock theta function; smallest parts functions; congruences modulo powers of 5; Eisenstein series; CONGRUENCES; PARTITIONS
Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
Type
journal article