AbstractLet
N≥1
be squarefree with
(N,6)=1
. Let
cϕN(n)
denote the number of N-colored generalized Frobenius partitions of n introduced by Andrews in 1984, and
P(n)
denote the number of partitions of n. We prove
cϕN(n)=d∣N∑N/d⋅P(d2Nn−24d2N2−d2)+b(n),
where
C(z):=(q;q)∞N∑n=1∞b(n)qn
is a cusp form in
S(N−1)/2(Γ0(N),χN)
. This extends and strengthens earlier results of Kolitsch and Chan–Wang–Yan treating the case when N is a prime. As an immediate application, we obtain an asymptotic formula for
cϕN(n)
in terms of the classical partition function
P(n)
.</jats:p