论文标题
在有限的场锥限制性猜想中，在四个维度和发射率几何形状中的应用中
On the finite field cone restriction conjecture in four dimensions and applications in incidence geometry
论文作者
论文摘要
本文的第一个目的是将有限的场锥限制猜想在四个维度上以$ -1 $ $非方面的形式解决。第二个是通过限制理论引入一种新的方法来研究发病率问题。更确切地说，使用锥体限制估计值，我们将证明与小尺寸的球体集相关的复杂值函数相关的尖锐点球发生界限。我们与特定功能的发病率界限显着改善了Cilleruelo，Iosevich，Lund，Roche-Newton和Rudnev的结果。
The first purpose of this paper is to solve completely the finite field cone restriction conjecture in four dimensions with $-1$ non-square. The second is to introduce a new approach to study incidence problems via restriction theory. More precisely, using the cone restriction estimates, we will prove sharp point-sphere incidence bounds associated with complex-valued functions for sphere sets of small size. Our incidence bounds with a specific function improve significantly a result given by Cilleruelo, Iosevich, Lund, Roche-Newton, and Rudnev.
