New congruences for partitions related to mock theta functions

Wang, Liuquan

doi:10.1016/j.jnt.2016.11.018

Cited by 30 publications

(18 citation statements)

References 4 publications

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“…Recently, among other results, Wang [8] discovered some new congruences for p ω (n). Moreover, he pointed out that as a natural consequence of (1.14), we have ∞ n=0 spt ω (2n + 1)q n = (q 2 ; q 2 ) 8 ∞ (q; q) 5 ∞ .…”

Section: Introductionmentioning

confidence: 99%

The smallest parts function associated with $ω(q)$

Wang¹,

Yang²

2018

Preprint

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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 spt ω (n), which was introduced by Andrews, Dixit and Yee and associated with Ramanujan/Watson's third order mock theta function ω(q). The second one is spt C5 (n), which appeared in the work of Garvan and Jennings-Shaffer. Moreover, we confirm two conjectural congruences of Wang.

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Section: Introductionmentioning

confidence: 99%

The smallest parts function associated with $ω(q)$

Wang¹,

Yang²

2018

Preprint

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“…Recently, Andrews et al [1] studied the partition functions p ω (n) and p ν (n) associated to the third-order mock theta functions ω(q) and ν(q). Later, congruences for p ω (n) and p ν (n) were investigated (see [3,22]). Congruences satisfied by p ω (an + b) and p ν (an + b) are usually derived from their generating functions and identities between certain mock theta functions.…”

Section: Introductionmentioning

confidence: 99%

Overpartitions Related to the Mock Theta Function

Lin¹

2020

Bull. Aust. Math. Soc.

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Recently, Brietzke, Silva and Sellers [‘Congruences related to an eighth order mock theta function of Gordon and McIntosh’, J. Math. Anal. Appl.479 (2019), 62–89] studied the number $v_{0}(n)$ of overpartitions of $n$ into odd parts without gaps between the nonoverlined parts, whose generating function is related to the mock theta function $V_{0}(q)$ of order 8. In this paper we first present a short proof of the 3-dissection for the generating function of $v_{0}(2n)$ . Then we establish three congruences for $v_{0}(n)$ along certain progressions which are subsequences of the integers $4n+3$ .

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“…They also proved several congruences modulo 2 and infinite families of congruences modulo 4 and modulo 8 for p ω (n) and p ν (n). Motivated by the works in [5,7], Wang [28] and Cui, Gu and Hao [14] found many new congruences satisfied by p ω (n) and p ν (n) modulo 11 and modulo powers of 2 and 3. In particular, Wang [28] derived the following exact generating functions: .…”

Section: Introductionmentioning

confidence: 99%

“…Recently, the question was answered in affirmative by Bringmann, Jennings-Shaffer and Mahlburg [12]. Recently, Wang [28] and Cui, Gu and Hao [14] also found many new congruences satisfied by p ω (n), spt ω (n) and spt ω (n) modulo powers of 2 and 3. In particular, Wang [28] derived the following exact generating functions:…”

Section: Introductionmentioning

confidence: 99%