Year: 2026
Type: preprint
Abstract: A set of points $N\subseteq \mathbb{F}_q^d$ is a Nikodym set if, for any $x\in \mathbb{F}_q^d$, there is a line $\ell$ through $x$ such that $\ell\setminus\{x\}\subseteq N$. We conjecture that $|N|=q^d-O_d(q^{d/(d-1)})$ and prove it under an extra algebraic assumption.
Source: arXiv (Cornell University)
Authors: Chao, Ting-Wei, Yu, Hung-Hsun Hans
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7126023241
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