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An upper estimate for the lattice point enumerator

  • P. Gritzmann (a1) and J. M. Wills (a1)

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.

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