改进的抛物线高低法
An improved high-low method for the parabola
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中文总结 AI 辅助
本文改进Guth-Maldague-Wang高低法，通过正交展开和新型平方函数，获得抛物线离散限制常数尖锐估计及有理点加性能量无直径界，分别验证了近期两项研究成果。
中文摘要 AI 辅助
我们展示了Guth-Maldague-Wang高低法的一种改进，该方法产生了一个解耦定理，该定理给出了抛物线离散限制常数的尖锐估计，以及抛物线和圆上有理点三倍加性能量的无直径界。这些结果最近分别由Deng-Fan-Guo-Guo-Luo和Cushman-Demeter-Wu获得。该论证的新颖之处在于$F^3$的正交展开和一个新的平方函数，该函数还保留了修剪后丢弃的波包，从而产生新的更高效的高低引理。
英文摘要
We demonstrate a modification of the high-low method of Guth-Maldague-Wang that yields a decoupling theorem which gives the sharp estimate for the discrete restriction constant for the parabola and also a diameter-free bound for the three-fold additive energy of rational points on the parabola and circle. These results were recently obtained by Deng-Fan-Guo-Guo-Luo and Cushman-Demeter-Wu, respectively. The novel features in this argument are an orthogonal expansion of $F^3$ and a new square function that also keeps the wavepackets discarded after pruning, resulting in new and more efficient high and low lemmas.
发表机构
- North Carolina State University（北卡罗来纳州立大学）
- Mathematical Sciences Institute, Australian National University（澳大利亚国立大学数学科学研究所）
- Department of Mathematics, The Chinese University of Hong Kong（香港中文大学数学系）
- CNRS-ANU International Research Laboratory FAMSI (France Australia Mathematical Sciences and Interactions)（中法国际数学科学交互联合实验室）
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