Can I read Lattice Points and the Volume/area Ratio of Convex Bodies on EtoBox?

Lattice Points and the Volume/area Ratio of Convex Bodies by J. Bokowski; A. M. Odlyzko is a Mathematics article available to read on EtoBox.

What is Lattice Points and the Volume/area Ratio of Convex Bodies about?

## RATIO OF CONVEX BODIES Let K be a convex body in n-dimensional Euclidean space R" (n i> 2), V(K) > 0 its n-dimensional volume, A(K) its (n-1)-dimensional surface area, and L(K) the number of lattice points (points with integer coordinates) in the interior of K. We will be concerned with obtaining lower bounds for L(K) from lower bounds for the volume/area ratio V(K)/A (K), and upper bounds for V(K)/A (K) from upper bounds for L(K). These questions were first studied explicitly for n=2 by Bender [1] and Hammer [8, 9]. Wills [16] later considered the case of general n >12, and since then various additional results have been obtained by Bender [2], Hadwiger [6], Hammer [10], Odlyzko [13], Reich [14], and Wills [1%19]. Depending on whether one wishes to obtain bounds for V(K)/A(K) in terms ofL (K) or conversely, it is convenient to work either with defined for m and n integers, m>\_ 1, n>2, or with l (e, n) = min {L (K): V (K)/A (K) >1 c~, K = R"}, defined for n ~> 2 and ~ any positive real number. Let co, be the volume of the n-dimensional unit sphere. We will prove THEOREM. lf m and n are integers, m>~ 1, n~>2, and c~ is a positive real number, then n kco./ n\ co. / 2 and ¢o,n"c~

Who reads Lattice Points and the Volume/area Ratio of Convex Bodies?

Author

J. Bokowski; A. M. Odlyzko

Publisher

Springer; Springer-Verlag; Kluwer Academic Publishers; Springer Science and Business Media LLC (ISSN 0046-5755)

Published

1973

Language

EN

Field

Mathematics (Physical Sciences)