  For an arbitrary quiver Q and dimension vector d we prove that the dimension
of the space of cuspidal functions on the moduli stack of representations of Q
of dimension d over a finite field F_q is given by a polynomial in q with
rational coefficients. We define a variant of this polynomial counting
absolutely cuspidal functions, prove that it has integral coefficients and
conjecture that it has positive coefficients. In the case of totally negative
quivers (such as the g-loop quiver for g >1) we provide a closed formula for
these polynomials in terms of Kac polynomials.
