A new bound for finite field Besicovitch sets in four dimensions
| dc.creator | Tao, Terence | |
| dc.date | 2002-04-19 | |
| dc.date | 2002-09-10 | |
| dc.date.accessioned | 2026-07-07T04:47:57Z | |
| dc.date.available | 2026-07-07T04:47:57Z | |
| dc.description | Let $F$ be a finite field with characteristic greater than two. Define a \emph{Besicovitch set} in $F^4$ to be a set $P \subseteq F^4$ containing a line in every direction. The \emph{Kakeya conjecture} asserts that $|P| \approx |F|^4$. A result of Wolff establishes that $|P| \gtrsim |F|^3$. In this paper we improve this to $|P| \gtrapprox |F|^{3+\gain}$. On the other hand, we show that the bound of $|F|^3$ is sharp if we relax the assumption that the lines point in different directions. One new feature in the argument is the introduction of a small amount of basic algebraic geometry. | |
| dc.description | 28 pages, no figures, to appear, Pacific J. Math. More exposition, less typos | |
| dc.identifier | https://arxiv.org/abs/math/0204251 | |
| dc.identifier | http://arxiv.org/abs/math/0204251 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63865 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 42B25, 05C35 | |
| dc.title | A new bound for finite field Besicovitch sets in four dimensions | |
| dc.type | text |