Journal of the
Korean Mathematical Society
JKMS

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

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J. Korean Math. Soc.

Published online June 9, 2022

Copyright © The Korean Mathematical Society.

New Congruences For $\ell$-Regular Overpartitions

Ankita Jindal and Nabin K. Meher

Indian Statistical Institute Delhi, Birla Institute of Technology & Science Pilani, Hyderabad Campus

Abstract

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

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