On the size of kakeya sets in finite fields

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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 ... Web10 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 maximal functions associated to algebraic varieties W over finite fields F.

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

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 … 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 ... culver\u0027s plant city florida

On the size of Kakeya sets in ﬁnite ﬁelds - arXiv

WebKAKEYA-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. WebON THE SIZE OF KAKEYA SETS IN FINITE FIELDS ZEEVDVIR 1.Introduction Let𝔽denoteaﬁniteﬁeldof𝑞elements.AKakeya set(alsocalledaBesicovitch … WebON THE SIZE OF KAKEYA SETS IN FINITE FIELDS - Read online for free. Abstract. A Kakeya set is a subset of F n, where F is a finite field of q elements, that contain a line in every direction. In this paper, we show that the size of every Kakeya set is at least Cn · q n, where Cn depends only on n. This answers a question of Wolff [Wol99]. east palo alto sutter health

Introduction q Kakeya F K - Institute for Advanced Study

Conical Kakeya and Nikodym sets in finite fields - ScienceDirect

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 C n ⋅ q … east palo alto real estate marketWebSaraf 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. culver\u0027s pumpkin shake

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On the size of kakeya sets in finite fields

WebCiteSeerX - 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 … 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 ...

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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 … 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 …

WebDefinition 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: … Web30 de jul. de 2024 · Sharp density bounds on the finite field Kakeya problem @inproceedings{Bukh2024SharpDB, title= ... Improved lower bounds on the size of …

Web30 de jul. de 2024 · Finite field Kakeya and Nikodym sets in three dimensions. SIAM J. Discrete Math., 32(4):2836-2849, 2024. arXiv:1609.01048. An improved lower bound on the size of Kakeya sets over finite fields 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 …

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 ...

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 … culver\u0027s prices and menuWebON THE SIZE OF KAKEYA SETS IN FINITE FIELDS ZEEV DVIR Abstract. A Kakeya set is a subset of Fn, where Fis 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 ¢ qn, where Cn depends only on n. This answers a question of Wolﬀ [Wol99]. 1. Introduction east palo alto weather monthlyWeb1 de set. 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 … culver\u0027s plant city flWebOn the size of Kakeya sets in ﬁnite ﬁelds Zeev Dvir ∗ Abstract A Kakeya set is a subset of Fn, where F is a ﬁnite ﬁeld of q elements, that contains a line in every direction. In this … culver\u0027s radiant scheduleWebobservation that a product of Kakeya sets is also a Kakeya set. Corollary 1.1. For every integer n and every ǫ > 0 there exists a constant Cn,ǫ, de-pending only on n and ǫ such that any Kakeya set K ⊂ Fn satisﬁes K ≥ Cn,ǫ ·qn−ǫ, Proof. Observe that, for every integer r > 0, the Cartesian product Kr ⊂ Fn·r is also a Kakeya set. east palo alto to haywardWeb22 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 ... culver\u0027s plant city menuWeb14 de out. de 2024 · Read article at ArXiv. Simple proofs for Furstenberg sets over finite fields, Discrete Analysis 2024:22, 16 pp. A Kakeya set in R 2 is a subset that contains a unit line segment in every direction. A well-known result of Besicovitch states that there are Kakeya sets of measure zero. This has led to numerous further results and some … culver\u0027s racine flavor of the day