WebA Kakeya set is a subset of F n, where F is a finite field of q elements, that contains a line in every direction. In this paper we show that the size of every Kakeya set is at least C n ⋅ q … Web18 de set. de 2008 · We give improved lower bounds on the size of Kakeya and Nikodym sets over $\mathbb{F}_q^3$. We also propose a natural conjecture on the minimum number of points in the union of a not-too-flat set ...
On the size of Kakeya sets in finite fields - arXiv
WebNote that if K0ˆR2 is a Kakeya set, then K:= K0 [0;1]n 2 is a Kakeya set in Rn, and moreover, if K0has measure zero, then Kalso has measure zero, so Kakeya sets, even when considered in Rn, can be of arbitrarily small measure, given Besicovitch’s result. Thus, it is natural to ask if there’s any di erence between small Kakeya sets of di ... WebSaraf and M. Sudan , An improved lower bound on the size of Kakeya sets over finite fields, Anal. PDE, 1 ( 2008), pp. 375 -- 379 . Crossref ISI Google Scholar. 15. A. Warren and A. Winterhof , Conical Kakeya and Nikodym sets in finite fields, Finite Fields Appl., 59 ( 2024), pp. 185 -- 198 . Crossref ISI Google Scholar. 16. T. impp antwortbogen
Conical Kakeya and Nikodym sets in finite fields Request PDF
Web4 de jun. de 2024 · A Kakeya set contains a line in each direction. Dvir proved a lower bound on the size of any Kakeya set in a finite field using the polynomial method. We prove analogues of Dvir's result for non-degenerate conics, that is, parabolae and hyperbolae (but not ellipses which do not have a direction). We also study so-called … WebON THE SIZE OF KAKEYA SETS IN FINITE FIELDS ZEEVDVIR 1.Introduction Let𝔽denoteafinitefieldof𝑞elements.AKakeya set(alsocalledaBesicovitch … WebWe study subsets of the n -dimensional vector space over the finite field F q, for odd q, which contain either a sphere for each radius or a sphere for each first coordinate of the center. We call such sets radii spherical Kakeya sets and center spherical Kakeya sets, respectively. For n ≥ 4 we prove a general lower bound on the size of any ... impo women\\u0027s wedge shoes