NEW INFINITE FAMILIES OF RAMANUJAN-TYPE CONGRUENCES MODULO 9 FOR OVERPARTITION PAIRS

Let (pp) over bar (n) denote the number of overpartition pairs of n. Bringmann and Lovejoy (2008) proved that for n >= 0, (pp) over bar (3n + 2) equivalent to 0 (mod 3). They also proved that there are infinitely many Ramanuj an-type congruences modulo every power of odd primes for (pp) over bar (n). Recently, Chen and Lin (2012) established some Ramanujan-type identities and explicit congruences for (pp) over bar (n). Furthermore, they also constructed infinite families of congruences for (pp) over bar (n) modulo 3 and 5, and two congruence relations modulo 9. In this paper, we prove several new infinite families of congruences modulo 9 for (pp) over bar (n). For example, we find that for all integers k, n >= 0, (pp) over bar (2(6k)(48n + 20)) equivalent to (pp) over bar (26k (384n + 32)) equivalent to (pp) over bar (2(3k)(48n + 36)) equivalent to (mod 9).