New restriction estimates for the 3-d paraboloid over finite fields

被引：22
|
作者：
Lewko, Mark [1 ]
机构：
[1] Univ Calif Los Angeles, Dept Math, Los Angeles, CA 90024 USA
来源：
ADVANCES IN MATHEMATICS | 2015年 / 270卷
基金：
美国国家科学基金会;
关键词：
Fourier transform; Restriction conjecture; Finite field; Sum-product; EXTENSION-THEOREMS;
D O I：
10.1016/j.aim.2014.11.008
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We improve the range of exponents for the restriction problem for the 3-d paraboloid over finite fields. The key new ingredient is a variant of the Bourgain-Katz-Tao finite field incidence theorem derived from sum-product estimates. In prime order fields, we give an explicit relationship between the exponent in this incidence theorem and restriction estimates for the paraboloid. (C) 2014 Elsevier Inc. All rights reserved.
引用
收藏
页码：457 / 479
页数：23
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