On the arithmetic Kakeya conjecture of Katz and Tao. | LitMetric

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On the arithmetic Kakeya conjecture of Katz and Tao. | LitMetric

On the arithmetic Kakeya conjecture of Katz and Tao.

Ben Green Imre Z Ruzsa

Period Math Hung

2Alfred Rényi Institute, Reáltanoda utca 13-15., Budapest, 1053 Hungary.

Published: November 2018

The arithmetic Kakeya conjecture, formulated by Katz and Tao (Math Res Lett 6(5-6):625-630, 1999), is a statement about addition of finite sets. It is known to imply a form of the Kakeya conjecture, namely that the upper Minkowski dimension of a Besicovitch set in is . In this note we discuss this conjecture, giving a number of equivalent forms of it. We show that a natural finite field variant of it does hold. We also give some lower bounds.

Download full-text PDF	Source
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6528801	PMC
http://dx.doi.org/10.1007/s10998-018-0270-z	DOI Listing

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