  We explore the Fourier transform of the Heegaard Floer $d$-invariants, which
is particularly well-behaved with respect to connected sum. As corollaries, we
show that lens spaces are cancellable in the monoid of 3-manifolds up to
integer homology cobordism, and we recover a theorem of
Gonz\'alez-Acu\~na--Short on Alexander polynomials of knots with reducible
surgeries.
