Congruences for l-regular overpartitions into odd parts

In this paper, we study various arithmetic properties of the function (po) over bar (l)(n), which denotes the number of l-regular overpartitions of n into odd parts. We will prove several Ramanujan-like congruences and infinite families of congruences modulo 3 and 8 for <(po)over bar(3) and modulo 8 for <(po)over bar>(5). For example, we find that for all nonnegative integers alpha and n, <(po)over bar(3) (12n + 6) 0(mod 3), <(po)over bar(3)(12n + 10) 0 (mod 3), <(po)over bar(3)(72n + 60) 0(mod 3) and <(po)over bar>(5)(8 . 5(2 alpha+1)n + r(1) . 5(2 alpha)) 0(mod 8), where r(1) epsilon {11, 19}.