### Electronic Research Archive

2021, Issue 6: 4257-4268. doi: 10.3934/era.2021084

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

• Received: 01 June 2021 Revised: 01 September 2021 Published: 26 October 2021
• Primary: 11P83, 05A17

• Ramanujan introduced sixth order mock theta functions $\lambda(q)$ and $\rho(q)$ defined as:

\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*}

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.

Citation: Harman Kaur, Meenakshi Rana. Congruences for sixth order mock theta functions $\lambda(q)$ and $\rho(q)$[J]. Electronic Research Archive, 2021, 29(6): 4257-4268. doi: 10.3934/era.2021084

### Related Papers:

• Ramanujan introduced sixth order mock theta functions $\lambda(q)$ and $\rho(q)$ defined as:

\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*}

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. ###### 通讯作者: 陈斌, bchen63@163.com
• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142 1.604 0.8

Article outline

## Other Articles By Authors

• On This Site  DownLoad:  Full-Size Img  PowerPoint