J. Korean Math. Soc. 2022; 59(5): 945-962
Online first article June 9, 2022 Printed September 1, 2022
https://doi.org/10.4134/JKMS.j220011
Copyright © The Korean Mathematical Society.
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.
2020; 57(2): 471-487
2015; 52(2): 333-347
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