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On the number of lattice points in convex symmetric bodies and their duals. (English) Zbl 0752.52008
Isr. J. Math. 74, No. 2-3, 347-357 (1991); erratum ibid. 171, 443-444 (2009).
Let $$K\subset\mathbb{R}^ n$$ be a convex, centrally symmetric, bounded, absorbing set, $$vol(K)$$ its standard volume, $$K^*$$ its polar convex set, and $$\# (K\cap\mathbb{Z}^ n)$$ the number of lattice points in $$K$$. Authors prove that $$\# (K\cap\mathbb{Z}^ n)/(\# (K^*\cap\mathbb{Z}^ n)\text{vol}(K))$$ is bounded below and above by positive constants depending on $$n$$ but not on $$K$$, and they give various applications of this result.

##### MSC:
 52C07 Lattices and convex bodies in $$n$$ dimensions (aspects of discrete geometry)
##### Keywords:
convex body; polar body; lattice points
Full Text:
##### References:
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