The Steinhaus tiling problem and the range of certain quadratic forms

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We give a short proof of the fact that there are no measurable subsets of Euclidean space (in dimension d > 2), which, no matter how translated and rotated, always contain exactly one integer lattice point. In dimension d=2 (the original Steinhaus problem) the question remains open.

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Classical Analysis and ODEs, Metric Geometry, Number Theory, 52C22; 11E25

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http://salesiana.dossiersoluciones.com/handle/123456789/59986

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0009207
 http://arxiv.org/abs/math/0009207

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arXiv