Arithmetic properties for l-regular partition functions with distinct even parts

Let Ped(l)(n) denote the number of l-regular partitions of a positive integer n into distinct even parts. In this paper, we prove congruences modulo 2 and 4 for Ped(l)(n) when l=3, 5, 7 and 11. We also prove the infinite families of congruences modulo 9, 12, 18 and 24 for Ped(9)(n). For example, for any alpha >= 0 and 1 <= r <= p - 1, we have Ped(9) (24 . p(2 alpha+1)(pn + r) + 10 . p(2 alpha+2) + 1) (math) 0(mod 24).