Congruences for frobenius partitions

The partition function p(n) has several celebrated congruence properties which reflect the action of the Hecke operators on certain holomorphic modular forms. In this article similar congruences are proved for c(3)(n), the number of generalized Frobenius partitions of n with 3 colors. We prove (1) c(3)(63n + 50) = 0 mod 7, (2) c(3)(5n + 2) = p(5n + 2/3) mod 5, exept when n = 3T(m) and T-m = m(m + 1)/2 is the mth triangular number, and (3) c(3)(15T(m) + 2) = (-1)(m) (m + 3) mod 5. Congruences (2) and (3) are analogous to Euler's pentagonal number theorem. These congruences are proved by constructing holomorphic modular forms which inherit related congruence properties which are verified computationally via Sturm's criterion. (C) 1996 Academic Press, Inc.