Averaging operators over nondegenerate quadratic surfaces in finite fields

2012/09/06 by Doowon Koh, Koh, Doowon
Computer Science · Mathematics · #43A15 #43A32 #Algebraic Geometry and Number Theory #Analysis of PDEs (math.AP) #Analytic Number Theory Research #Coding theory and cryptography #FOS: Mathematics #math.AP #msc:43A15 #msc:43A32

paper · pdf · doi:10.48550/arxiv.1209.1220

14 pages, 1 figure, abstract is rewritten and statements were shorten

openalex publication_date 2012/09/06 · arxiv created 2012/12/21 · arxiv updated 2012/12/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study mapping properties of the averaging operator related to the variety V=x∈ \mathbb F_q^d: Q(x)=0, where Q(x) is a nondegenerate quadratic polynomial over a finite field \mathbb F_q with q elements. This paper is devoted to eliminating the logarithmic bound appearing in the paper of Koh and Shen. As a consequence, we settle down the averaging problems over the quadratic surfaces V in the case when the dimensions d≥ 4 are even and V contains a d/2-dimensional subspace.

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