An improved high-low method for the parabola
Zane Kun Li, Po-Lam Yung
Source 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 and a new square function that also keeps the wavepackets discarded after pruning, resulting in new and more efficient high and low lemmas.
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