Arithmetic properties of the 2-color overpartition function p_ℓ(n)

2026/07/18 by H. S. Sumanth Bharadwaj, N. Sujatha, S. Chandankumar
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Abstract

We derive general families of Ramanujan-type congruences for the function p_ℓ(n), which counts the 2-color overpartitions of n in which one of the colors appears only in parts that are multiples of ℓ. For example, for all n≥0 we prove that p₄(32n+28)≡ 0 \pmod512.

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