Given a polynomial q(z) := a 0 + a 1 z + · · · + anz n and a vector of positive weights w = (w 0 , w 1 , . . . , wn), define the w-weighted lp-norm of q as lp,w[q] := n k=02010 Mathematics Subject Classification. Primary, 11N45; secondary, 11C08, 60G55, 30C15, 26C10.