Arithmetic properties of 2^α-Regular overpartition pairs

2025/02/24 by B., Hemanthkumar, S, Sumanth Bharadwaj H.
#05A17 #11P83 (Primary) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2502.17312

Abstract

Recently, several mathematicians have investigated various partition functions with the goal of discovering Ramanujan-type congruences. One such function is B_2^α(n), which represents the number of 2^α-regular overpartition pairs of n. In this context, we establish Ramanujan-type congruences modulo powers of 2 for this function. For instance, we prove that B_2^α(2^α+β+1(n+1)) ≡ 0\pmod2^3β+5 for all n, β≥ 0, α∈ ℕ.

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