2025/07/02 by N. K. Meher, Nabin Kumar Meher, Meher, N. K. +1 · 1 citation
Mathematics · #05A17 #11P83 #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Mathematical functions and polynomials #Number Theory (math.NT) #math.NT #msc:05A17 #msc:11P83
paper · pdf · doi:10.48550/arxiv.2507.01529
corrected version is uploaded
openalex publication_date 2025/07/02 · openalex created_date 2025/10/10 · arxiv created 2026/07/31 · arxiv updated 2026/08/03 · openalex updated_date 2026/08/03
Recently, Nadji, Ahmia and Ramírez \citeNadji2025 investigate the arithmetic properties of Bℓ1,ℓ2(n), the number of overpartitions where no part is divisible by ℓ1 or ℓ2 with gcd(ℓ1,ℓ2)=1 and ℓ1,ℓ2>1. Specifically, they established congruences modulo 3 and powers of 2 for the pairs of (ℓ1,ℓ2)∈\(4,3),(4,9),(8,3),(8,9)\, using the concept of generating functions, dissection formulas and Smoot's implementation of Radu's Ramanujan-Kolberg algorithm. After that, Alanazi, Munagi and Saikia \citeAlanazi2024 studied and found some congruences for the pairs of (ℓ1,ℓ2)∈\(2,3),(4,3),(2,5),(3,5),(4,9),(8,27), (16,81)\ using the theory of modular forms and Radu's algorithm. Recently Paudel, Sellers and Wang \citePaudel2025 extended several of their results and established infinitely many families of new congruences. In this paper, we find infinitely many families of congruences modulo 3 and powers of 2 for the pairs (ℓ1,ℓ2) ∈ \(2,9),(5,2),(5,4),(8,3)\ and in general for (5,2t) ∀ t≥3 and for (3,2t), (4,3t) ∀ t≥2, using the theory of Hecke eigenform, an identity due to Newman and the concept of dissection formulas and generating functions.