Nullstellenverteilung zweier konvexgeometrischer Polynome. (Distribution of zeroes of two convexgeometrical polynomials.) (Q917928)

For a convex body K in \({\mathbb{R}}^ d\), let \(V_ i(K)\) denote its ith intrinsice volume, and for a convex lattice polytope P, let \(G(P):=card(P\cap {\mathbb{Z}}^ d)\). In analogy to the Steiner polynomial \(V_ n(K+\lambda B^ d)=\sum^{d}_{i=0}\kappa_ iV_{d- i}(K)\ell^ i\) (\(\lambda\geq 0\), \(B^ d=unit\) ball in \({\mathbb{R}}^ d\), \(\kappa_ i=V_ i(B^ i))\), which plays a role in the theory of convex bodies, the author investigates the polynomials \(W(\lambda K)=\sum^{d}_{i=0}V_ i(K)\lambda^ i\) and \(G(\lambda P)=\sum^{d}_{i=0}G_ i(P)\lambda^ i\). He is particularly interested in their zeroes in the complex plane and relations to geometric properties.