Minkowski's successive minima and the zeros of a convexity-function (Q748898)

For a convex body \(K\subset E^ d\) let \(V_ i(K)\), \(i=0,1,...,d\) denote its normalized quermassintegrals. It is shown that there are several inequalities between the zeros of the polynomial \(W(\lambda K)=\sum^{d}_{i=0}V_ i(\lambda K)=\sum^{d}_{i=0}V_ i(K)\lambda^ i\) and Minkowski's successive minima.