The Fourier restriction and Kakeya problems over rings of integers modulo $N$

TL;DR

This paper investigates Fourier restriction and Kakeya problems over the ring of integers modulo N, revealing similarities with Euclidean cases and contrasting with finite field results.

Contribution

It introduces a novel analysis of these problems over rings of integers modulo N, expanding understanding beyond finite fields.

Findings

Similarities with Euclidean Fourier restriction and Kakeya problems

Contrasts with known finite field results

Provides new insights into structure over rings of integers

Abstract

The Fourier restriction phenomenon and the size of Kakeya sets are explored in the setting of the ring of integers modulo $N$ for general $N$ and a striking similarity with the corresponding euclidean problems is observed. One should contrast this with known results in the finite field setting.