Some Congruences for Overpartitions with Restriction
For any given positive integers m and n let pm n denote the number of overpartitions of n with no parts divisible by 4 m and only the parts congruent to m modulo 2 m overlined. In this paper, we prove Ramanujan type congruences modulo 2 for pm n by applying q series and Ramanujan's theta function identities.