Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Li, Zane Kun, Yung, Po-Lam
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214771321