Inequalities for convex bodies and polar reciprocal lattices in \(\mathbb{R}^ n\)
For a lattice \(L\) and an \(o\)-symmetric convex body in \(\mathbb{R}^ n\) let \(\lambda_ i (L, U)\) denote Minkowski's successive minima. Upper bounds are established for \(\lambda_ i (L, U) \lambda_{n-i +1} (L^*, V)\) where \(L^*\) is the dual lattice of \(L\) and \(U\), \(V\) are unit balls of the spaces \(l^ n_ p\), \(1\leq p\leq \infty\). The upper bounds are compared with known lower bounds.
scientific article; zbMATH DE number 735346