The Spherical Kakeya Problem in Finite Fields

DOI10.1137/19M1293788zbMath1453.52016arXiv2004.00904OpenAlexW3112058064MaRDI QIDQ5139665

Audie Warren, Arne Winterhof, Mehdi Makhul

Publication date: 10 December 2020

Published in: SIAM Journal on Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2004.00904

zbMATH Keywords

finite fieldsdiagonal equationssphereslinear spacesKakeya problem

Mathematics Subject Classification ID

Finite fields and commutative rings (number-theoretic aspects) (11T99) Combinatorial aspects of finite geometries (05B25) Erd?s problems and related topics of discrete geometry (52C10)

Cites Work

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• On a variant of the Kakeya problem in \(\mathbb{R}\)
• On the size of Kakeya sets in finite vector spaces
• Kakeya sets in finite affine spaces
• An improved lower bound on the size of Kakeya sets over finite fields
• On some variants of the Kakeya problem
• Conical Kakeya and Nikodym sets in finite fields
• On the size of Kakeya sets in finite fields
• THE KAKEYA SET AND MAXIMAL CONJECTURES FOR ALGEBRAIC VARIETIES OVER FINITE FIELDS
• Extension theorems for spheres in the finite field setting
• A Kakeya-type problem for circles
• Extremal Bases for Finite Cyclic Groups
• Extensions to the Method of Multiplicities, with Applications to Kakeya Sets and Mergers

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