Some Congruences for Overpartitions with Restriction

For any given positive integersmand n, let pm(n) denote the number of overpartitions of n with no parts divisible by 4mand only the parts congruent tommodulo 2moverlined. In this paper, we prove Ramanujan-type congruences modulo 2 for pm(n) by applying q-series and Ramanujan’s theta-function identities.