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arXiv · 1903.03904

Extension theorems for Hamming varieties over finite fields

Daewoong Cheong·Doowon Koh·Thang Pham
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Abstract

We study the finite field extension estimates for Hamming varieties $H_j, j\in \mathbb F_q^*,$ defined by $H_j=\{x\in \mathbb F_q^d: \prod_{k=1}^d x_k=j\},$ where $\mathbb F_q^d$ denotes the $d$-dimensional vector space over a finite field $\mathbb F_q$ with $q$ elements. We show that although the maximal Fourier decay bound on $H_j$ away from the origin is not good, the Stein-Tomas $L^2\to L^r$ extension estimate for $H_j$ holds.

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Daewoong Cheong, Doowon Koh, Thang Pham. 2019-03-10. Extension theorems for Hamming varieties over finite fields. https://arxiv.org/abs/1903.03904

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