site stats

On the size of kakeya sets in finite fields

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 https://cocoeastcorp.com

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

ON THE SIZE OF KAKEYA SETS IN FINITE FIELDS Introduction

Category:The Spherical Kakeya Problem in Finite Fields SIAM Journal on ...

Tags:On the size of kakeya sets in finite fields

On the size of kakeya sets in finite fields

The Spherical Kakeya Problem in Finite Fields SIAM Journal on ...

WebAbstract. A Kakeya set is a subset of n, where 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 … Web16 de abr. de 2008 · In this paper, we study the size of local Kakeya sets with respect to subsets of Fn and obtain upper and lower bounds for the minimum size of a (local) …

On the size of kakeya sets in finite fields

Did you know?

Web1 de set. de 2024 · 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 ... Web18 de ago. de 2008 · Download a PDF of the paper titled Improved lower bound on the size of Kakeya sets over finite fields, by Shubhangi Saraf and Madhu Sudan. PDF; …

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 Cn · q … WebIn a recent breakthrough, Dvir showed that every Kakeya set in Fn must have cardinality at least cn F n, where cn≈1∕n!. We improve this lower bound to βn F ... 2008 An improved lower bound on the size of Kakeya sets over finite fields. Shubhangi Saraf, Madhu Sudan. Anal. PDE 1(3): 375-379 (2008). DOI: 10.2140/apde ...

Web24 de ago. de 2024 · Let \mathbb {F} be a finite field consisting of q elements and let n \ge 1 be an integer. In this paper, we study the size of local Kakeya sets with respect to … 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 …

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, for any ǫ> 0, that the size of every Kakeya set is …

impp antwortbogen psychotherapieWebCiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): A 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, for any ǫ> 0, that the size of every Kakeya set is at least Cn,ǫ · q n−ǫ, where Cn,ǫ depends only on n and ǫ. This improves the previously best … impp antwortbogen musterWeb10 de dez. de 2009 · Using the polynomial method of Dvir [On the size of Kakeya sets in finite fields. Preprint], we establish optimal estimates for Kakeya sets and Kakeya … lith catWeb22 de fev. de 2013 · PDF For a finite field GF(q) a Kakeya set K is a subset of GF(q)^n that contains a line in every direction. This paper derives new upper bounds on the... Find, read and cite all the research ... imp panel wall anchorsWebKAKEYA-TYPE SETS IN LOCAL FIELDS WITH FINITE RESIDUE FIELD - Volume 62 Issue 2. Skip to main content Accessibility help We use cookies to distinguish you from other users and to provide you with a better experience on our websites. ... On the size of Kakeya sets in finite fields. J. lith clx l48WebWe give improved lower bounds on the size of Kakeya and Nikodym sets over $\\Bbb{F}_q^3$. We also propose a natural conjecture on the minimum number of points in the union of a not-too-flat set of lines in $\\Bbb{F}_q^3$ and show that this conjecture implies an optimal bound on the size of a Nikodym set. lithcoWebDefinition 1 (Kakeya Set) A set K ⊆ F n is said to be a Kakeya set in F n, if for every b ∈ F n, there exists a point a ∈ F n such that for every t ∈ F, the point a + t · b ∈ K. We show: … lithbridge