Journal of the
Korean Mathematical Society

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008



J. Korean Math. Soc. 2022; 59(5): 945-962

Online first article June 9, 2022      Printed September 1, 2022

Copyright © The Korean Mathematical Society.

New congruences for $\ell$-regular overpartitions

Ankita Jindal, Nabin K. Meher

Delhi, S. J. S. Sansanwal Marg; Pilani, Hyderbad 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 [15].

Keywords: Partition functions, regular overpartitions, theta function, congruences

MSC numbers: Primary 11P83; Secondary 05A17, 05A15

Supported by: The first author is supported by ISI Delhi Post doctoral fellowship. The second author is thankful to BITS Pilani, Hyderabad campus for providing warm hospitality, nice facilities for research and computing facility. The second author is supported by ISI Delhi Post doctoral fellowship.