Arithmetic properties of l-regular overpartition pairs

In this paper, we investigate the arithmetic properties of l-regular overpartition pairs. Let (B) over bar (l)(n) denote the number of l-regular overpartition pairs of n. We will prove the number of Ramanujan-like congruences and infinite families of congruences modulo 3, 8, 16, 36, 48, 96 for (B) over bar (3)(n) and modulo 3, 16, 64, 96 for (B) over bar (4)(n). For example, we find that for all nonnegative integers a and n, (B) over bar (3)(3(alpha)(3n + 2)) equivalent to 0 (mod 3), (B) over bar (3)(3(alpha)(6n + 4)) equivalent to 0 (mod 3), and (B) over bar (4) (8n + 7) equivalent to 0 (mod 64).