J. Korean Math. Soc.
Published online June 9, 2022
Copyright © The Korean Mathematical Society.
Ankita Jindal and Nabin K. Meher
Indian Statistical Institute Delhi, Birla Institute of Technology & Science Pilani, Hyderabad Campus
For a positive integer $\ell,$ $\overline{A}_{\ell}(n)$ denotes the number of overpartitions of $n$ into parts not divisible by $\ell.$ In this article, we find certain Ramanujan-type congruences for $\overline{A}_{ r \ell}(n),$ when $r\in\{8, 9\}$ and we deduce infinite families of congruences for them. Furthermore, we also obtain Ramanujan-type congruences for $\overline{A}_{ 13}(n)$ by using an algorithm developed by Radu and Sellers \cite{Radu2011}.
Keywords: Partition functions, Regular overpartitions, Theta function, Congruences
MSC numbers: Primary 11P83, Secondary 05A17, 05A15
2022 © The Korean Mathematical Society. Powered by INFOrang Co., Ltd