Abstract

In a recent breakthrough, Dvir showed that every Kakeya set in Fⁿ must have cardinality at least c_n|F|ⁿ, where c_n ≈ 1 ∕ n!. We improve this lower bound to βⁿ|F|ⁿ for a constant β > 0. This pins down the correct growth of the constant c_n as a function of n (up to the determination of β).

Keywords

Kakeya set, finite fields, polynomial method

Mathematical Subject Classification

Primary: 52C17

Secondary: 05B25

Authors