New Arithmetic Properties for Overpartitions where Nonoverlined Parts are ℓ-Regular

Abstract

In this paper, we study the partition functions Rℓ∗¯(n), which count the number of overpartitions of n where the non-overlined parts are ℓ-regular for a given ℓ. Using elementary techniques, as well as the theory of modular forms, we establish several new arithmetic properties, including infinite families of congruences for these functions. © Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2026.