Arithmetic properties of l-regular overpartition pairs

作者：Naika Megadahalli Siddanaika Mahadeva; Shivashankar Chandrappa

来源：Turkish Journal of Mathematics, 2017, 41(3): 756-774.

DOI：10.3906/mat-1512-62

• Congruences
• theta function
• overpartition pair
• regular partition

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).

• 出版日期2017