  A Fourier transform technique is introduced for counting the number of
solutions of holomorphic moment map equations over a finite field. This in turn
gives information on Betti numbers of holomorphic symplectic quotients. As a
consequence simple unified proofs are obtained for formulas of Poincare
polynomials of toric hyperkahler varieties, Poincare polynomials of Hilbert
schemes of points and twisted ADHM spaces of instantons on C^2 and Poincare
polynomials of all Nakajima quiver varieties. As an application, a proof of a
conjecture of Kac on the number of absolutely indecomposable representations of
a quiver is announced.
