English

A short proof of $\ell^2$ decoupling for the moment curve

Number Theory 2023-09-12 v3 Classical Analysis and ODEs

Abstract

We give a short and elementary proof of the 2\ell^{2} decoupling inequality for the moment curve in Rk\mathbb{R}^k, using a bilinear approach inspired by the nested efficient congruencing argument of Wooley (arXiv:1708.01220).

Keywords

Cite

@article{arxiv.1912.09798,
  title  = {A short proof of $\ell^2$ decoupling for the moment curve},
  author = {Shaoming Guo and Zane Kun Li and Po-Lam Yung and Pavel Zorin-Kranich},
  journal= {arXiv preprint arXiv:1912.09798},
  year   = {2023}
}

Comments

v3: fixed up issues about weights in the published version. Weights in Section 3 are now required to decay a bit faster at infinity, and proofs of properties of weights are now given in an Appendix