Congruences for overpartitions with ${\ell}$-regular nonoverlined parts

Let $\overline{R_{\ell}^{*}}$ denote the number of overpartitions of $n$ where nonoverlined parts are $\ell$-regular and overlined parts are unrestricted. In this paper, we establish several Ramanujan like congruences and infinite families of congruences for $\overline{R_{\ell}^{*}}$ for $\ell=2k, 5, 6$ and $8k$. For example, for all $n\geq 0$ $$\overline{R_{184}^{*}}(16n+15)\equiv 0\pmod{1472}.$$

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Publication Details

Journal
Functiones et Approximatio Commentarii Mathematici
Published
2025-06-16
DOI
https://doi.org/10.7169/facm/241226-5-5
Primary Topic
Advanced Mathematical Identities
Type
article
Field-Weighted Citation Impact
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article

Congruences for overpartitions with ${\ell}$-regular nonoverlined parts

S. Chandankumar, C. Shivashankar, K. C. Ajeyakashi
Functiones et Approximatio Commentarii Mathematici
Advanced Mathematical Identities
article

Congruences for overpartitions with ${\ell}$-regular nonoverlined parts

S. Chandankumar, C. Shivashankar, K. C. Ajeyakashi
article en

Abstract

Let $\overline{R_{\ell}^{*}}$ denote the number of overpartitions of $n$ where nonoverlined parts are $\ell$-regular and overlined parts are unrestricted. In this paper, we establish several Ramanujan like congruences and infinite families of congruences for $\overline{R_{\ell}^{*}}$ for $\ell=2k, 5, 6$ and $8k$. For example, for all $n\geq 0$ $$\overline{R_{184}^{*}}(16n+15)\equiv 0\pmod{1472}.$$

Functiones et Approximatio Commentarii MathematiciVol. 74(1)
Reduced inequalities
Openalex Percentile: Top 81%
Advanced Mathematical Identities
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Congruences for overpartitions with ${\ell}$-regular nonoverlined parts — S. Chandankumar, C. Shivashankar, et al. · Functiones et Approximatio Commentarii Mathematici (2025) | TGRS Research Map | TGRS