Generating functions and congruences for some partition functions related to mock theta functions

Baruah, Nayandeep Deka; Begum, Nilufar Mana

doi:10.1142/s1793042120500220

Cited by 9 publications

(3 citation statements)

References 28 publications

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“…Recently, Baruah and Begum [4] further investigated the exact generating function concerning spt ω (n). More precisely, they proved that…”

Section: Introductionmentioning

confidence: 99%

A conjecture of Baruah and Begum on the smallest parts function of restricted overpartitions

Tang¹

2022

Preprint

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In 2017, Andrews, Dixit, Schultz and Yee introduced the function spt ω (n), which denotes the number of smallest parts in the overpartitions of n in which the smallest part is always overlined and all odd parts are less than twice the smallest part. Recently, Baruah and Begum established several internal congruences and congruences modulo small powers of 5 for spt ω (n). Moreover, they conjectured a family of internal congruences modulo any powers of 5 and two families of congruences modulo any even powers of 5. In this paper, we confirm three families of congruences due to Baruah and Begum.

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“…Recently, Baruah and Begum [4] further investigated the exact generating function concerning spt ω (n). More precisely, they proved that…”

Section: Introductionmentioning

confidence: 99%

A conjecture of Baruah and Begum on the smallest parts function of restricted overpartitions

Tang¹

2022

Preprint

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“…The nodes (1,1), (1,2), (1,3), (1,4), (1,5), (2,1), (2,2), and (3, 1) have hook numbers 7, 5, 3, 2, 1, 3, 1, and 1, respectively. Since none of these is a multiple of 4, so λ is a 4-core.…”

Section: Introductionmentioning

confidence: 99%

Results on some partition functions arising from certain relations involving the Rogers-Ramanujan continued fractions

Baruah¹,

Begum²,

Das³

2020

Preprint

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“…In 2017, Fathima and Pore [4] obtained a number of congruences for p ω (n) and p ν (n) modulo 20 and some infinite families of congruences modulo 2. In the sequel, Baruah and Begum [2] in 2019 established many congruences for the same partition functions modulo powers of 5.…”

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confidence: 99%

Congruences for sixth order mock theta functions $ \lambda(q) $ and $ \rho(q) $

Kaur

Rana

2021

era

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Ramanujan introduced sixth order mock theta functions <inline-formula><tex-math id="M3">\begin{document}$ \lambda(q) $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M4">\begin{document}$ \rho(q) $\end{document}</tex-math></inline-formula> defined as:<disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{align*} \lambda(q) & = \sum\limits_{n = 0}^{\infty}\frac{(-1)^n q^n (q;q^2)_n}{(-q;q)_n},\\ \rho(q) & = \sum\limits_{n = 0}^{\infty}\frac{ q^{n(n+1)/2} (-q;q)_n}{(q;q^2)_{n+1}}, \end{align*} $\end{document} </tex-math></disp-formula>listed in the Lost Notebook. In this paper, we present some Ramanujan-like congruences and also find their infinite families modulo 12 for the coefficients of mock theta functions mentioned above.

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Generating functions and congruences for some partition functions related to mock theta functions

Cited by 9 publications

References 28 publications

A conjecture of Baruah and Begum on the smallest parts function of restricted overpartitions

A conjecture of Baruah and Begum on the smallest parts function of restricted overpartitions

Results on some partition functions arising from certain relations involving the Rogers-Ramanujan continued fractions

Congruences for sixth order mock theta functions $ \lambda(q) $ and $ \rho(q) $

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