SOME NEW INFINITE FAMILIES OF CONGRUENCES MODULO 3 FOR OVERPARTITIONS INTO ODD PARTS

Let (p) over bar (o)(n) denote the number of overpartitions of n in which only odd parts are used. Some congruences modulo 3 and powers of 2 for the function (p) over bar (o)(n) have been derived by Hirschhorn and Sellers, and Lovejoy and Osburn. In this paper, employing 2-dissections of certain quotients of theta functions due to Ramanujan, we prove some new infinite families of Ramanujan-type congruences for (p) over bar (o)(n) modulo 3. For example, we prove that for n, alpha >= 0, (p) over bar (o)(4(alpha) (24n + 17)) equivalent to (p) over bar (o)(4(alpha) (24n +23)) equivalent to 0 (mod 3)