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An upper estimate for the lattice point enumerator

Published online by Cambridge University Press:  26 February 2010

P. Gritzmann  and
J. M. Wills
P. Gritzmann
Affiliation:
Math. Inst. Univ. Siegen, Hölderlinstr. 3, D-5900 Siegen, Fed. Rep. Germany.
J. M. Wills
Affiliation:
Math. Inst. Univ. Siegen, Hölderlinstr. 3, D-5900 Siegen, Fed. Rep. Germany.
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Extract

Since Minkowski [29] gave his famous lattice point theorem for centrally symmetric convex bodies, a theorem that turned out to be of fundamental importance in number theory, much effort has been made to obtain tight estimates for the number of lattice points of a given lattice in convex bodies in terms of the basic quermass-integrals Wo,…, Wd, whose eminent role shows in Hadwiger's functional theorem [14, 15, 16, see also 17, p. 221–225]. (For the discrete analogues of Wo,…, Wd see [2].) The present paper is concerned with an upper estimate of this kind.

Type
Research Article
Information
Mathematika , Volume 33 , Issue 2 , December 1986 , pp. 197 - 203
Copyright
Copyright © University College London 1986

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