Conjecture and improved extension theorems for paraboloids in the finite field setting

被引：5

作者：

Koh, Doowon ^{[1
]}

机构：

[1] Chungbuk Natl Univ, Dept Math, Cheongju 28644, Chungbuk, South Korea

来源：

MATHEMATISCHE ZEITSCHRIFT | 2020年 / 294卷 / 1-2期

基金：

新加坡国家研究基金会;

关键词：

Restriction theorem; Extension theorem; Paraboloid; Finite field; RESTRICTION;

D O I：

10.1007/s00209-019-02250-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the extension estimates for paraboloids in d-dimensional vector spaces over finite fields Fq with q elements. We use the connection between L2 based restriction estimates and Lp -> Lr extension estimates for paraboloids. As a consequence, we improve the L2 -> Lr extension results obtained by Lewko and Lewko (Proc Am Math Soc 140:2013-2028, 2012) in even dimensions d >= 6 and odd dimensions d=4l+3 for l is an element of N. Our results extend the consequences for 3-D paraboloids due to Lewko (Adv Math 270(1):457-479, 2015) to higher dimensions. We also clarifies conjectures on finite field extension problems for paraboloids.

引用

页码：51 / 69

页数：19

共 21 条

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