The p-adic Kakeya conjecture

2021/08/08 by Bodan Arsovski, Arsovski, Bodan · 2 citations
Mathematics · #advanced mathematical theories #Advanced Topology and Set Theory #Analytic Number Theory Research

paper · pdf · doi:10.48550/arxiv.2108.03750

Abstract

We prove that all bounded subsets of ℚ_pⁿ containing a line segment of unit length in every direction have Hausdorff and Minkowski dimension n. This is the analogue of the classical Kakeya conjecture with ℝ replaced by ℚ_p.

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• High-low method and p-adic Furstenberg set over the plane
• The Oddtown problem modulo a composite number

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