Reversing a Philosophy: From Counting to Square Functions and Decoupling
Publication in refereed journal

香港中文大學研究人員
替代計量分析
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其它資訊
摘要Breakthrough work of Bourgain, Demeter, and Guth recently established that decoupling inequalities can prove powerful results on counting integral solutions to systems of Diophantine equations. In this note we demonstrate that in appropriate situations this implication can also be reversed. As a first example, we observe that a count for the number of integral solutions to a system of Diophantine equations implies a discrete decoupling inequality. Second, in our main result we prove an L2n square function estimate (which implies a corresponding decoupling estimate) for the extension operator associated to a non-degenerate curve in Rn. The proof is via a combinatorial argument that builds on the idea that if γ is a non-degenerate curve in Rn, then as long as x1,…,x2n are chosen from a sufficiently well-separated set, then γ(x1)+⋯+γ(xn)=γ(xn+1)+⋯+γ(x2n) essentially only admits solutions in which x1,…,xn is a permutation of xn+1,…,x2n.
著者Philip T. Gressman, Shaoming Guo, Lillian B. Pierce, Joris Roos, Po-Lam Yung
期刊名稱Journal of Geometric Analysis
出版年份2021
月份7
卷號31
期次7
頁次7075 - 7095
國際標準期刊號1050-6926
電子國際標準期刊號1559-002X
語言美式英語

上次更新時間 2021-28-11 於 00:20