An algebraic geometry version of the Kakeya problem

DOI10.1016/j.ffa.2015.09.005zbMath1328.14085arXiv1410.3701OpenAlexW2162948286MaRDI QIDQ897330

Kaloyan Slavov

Publication date: 17 December 2015

Published in: Finite Fields and their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1410.3701

zbMATH Keywords

permutation polynomialsKakeya problemaffine polynomialsimage set on \(F_q\)-pointsindecomposable polynomialsLang-Weil boundnumber of irreducible components of a varietyreducibility of polynomials in several variables

Mathematics Subject Classification ID

Finite ground fields in algebraic geometry (14G15) Finite geometry and special incidence structures (51E99) Configurations and arrangements of linear subspaces (14N20)

Related Items (2)

Variants of the Kakeya problem over an algebraically closed field ⋮ Factorization type probabilities of polynomials with prescribed coefficients over a finite field

Cites Work

• Variants of the Kakeya problem over an algebraically closed field
• An improved lower bound on the size of Kakeya sets over finite fields
• Reducibility of polynomials in two variables
• Bounds for fixed point free elements in a transitive group and applications to curves over finite fields
• Linearized polynomials and permutation polynomials of finite fields
• Recent progress on the Kakeya conjecture
• An improved bound for Kakeya type maximal functions
• Algebraic combinatorial geometry: the polynomial method in arithmetic combinatorics, incidence combinatorics, and number theory
• On the size of Kakeya sets in finite fields
• Sur le nombre des valeurs distinctes d'un polynôme à coefficients dans un corps fini
• Number of Points of Varieties in Finite Fields
• On the number of distinct values of a polynomial with coefficients in a finite field
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