The multiplier of a non-parabolic orbit of a map $z\to z^2+c$ can be extended by means of analytic continuation to a multiple-valued algebraic function on the space of quadratic polynomials $z^2+c$. We show that as the period of the periodic orbit increases to infinity, the critical points of the multiplier map equidistribute on the boundary of the Mandelbrot set. This is joint work with I.Gorbovickis.