Congruences modulo 8 for (2,k)-regular overpartitions for odd k>1

In this paper, we study various arithmetic properties of the function p¯¯¯2,k(n), which denotes the number of (2,k)-regular overpartitions of n with odd k>1. We prove several infinite families of congruences modulo 8 for p¯¯¯2,k(n). For example, we find that for all non-negative integers β,n and k≡1(mod8), p¯¯¯2,k(21+β(16n+14))≡ 0(mod8)