论文标题
在晶格的距离能量上渐近估计
Asymptotic estimate on the distance energy of lattices
论文作者
论文摘要
由于L. Guth和N. Katz在飞机上的Erdos不同距离问题上的众所周知的突破，因此人们的方法及其Elekes-Sharir框架引起了感兴趣的主流。简而言之，他们研究了框架中的第二刻。人们可能会怀疑较高的时刻是否会更有效。在本文中，我们表明，任何较高的时刻都会使期望失败。此外，我们表明第二时刻给出了更高维度的最佳估计。
Since the well-known breakthrough of L. Guth and N. Katz on the Erdos distinct distances problem in the plane, mainstream of interest is aroused by their method and the Elekes-Sharir framework. In short words, they study the second moment in the framework. One may wonder if higher moments would be more efficient. In this paper, we show that any higher moment fails the expectation. In addition, we show that the second moment gives optimal estimate in higher dimensions.
