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2019 Discrete analogues of John's theorem
Sören Lennart Berg, Martin Henk
Mosc. J. Comb. Number Theory 8(4): 367-378 (2019). DOI: 10.2140/moscow.2019.8.367

Abstract

As a discrete counterpart to the classical theorem of Fritz John on the approximation of symmetric n-dimensional convex bodies K by ellipsoids, Tao and Vu introduced so called generalized arithmetic progressions P(A,b)n in order to cover (many of) the lattice points inside a convex body by a simple geometric structure. Among others, they proved that there exists a generalized arithmetic progressions P(A,b) such that P(A,b)Kn P(A,O(n)3n2b). Here we show that this bound can be lowered to nO(lnn) and study some general properties of so called unimodular generalized arithmetic progressions.

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Sören Lennart Berg. Martin Henk. "Discrete analogues of John's theorem." Mosc. J. Comb. Number Theory 8 (4) 367 - 378, 2019. https://doi.org/10.2140/moscow.2019.8.367

Information

Received: 14 April 2019; Revised: 27 May 2019; Accepted: 16 June 2019; Published: 2019
First available in Project Euclid: 29 October 2019

zbMATH: 07126249
MathSciNet: MR4026544
Digital Object Identifier: 10.2140/moscow.2019.8.367

Subjects:
Primary: 11H06, 52C07
Secondary: 52A40

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.8 • No. 4 • 2019
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