English

A remark on the mean value inequalities related to Waring's problem

Classical Analysis and ODEs 2023-09-22 v1 Number Theory

Abstract

Assuming some pointwise estimates on certain Weyl's sum, we prove the sharp estimates of the mean value associated to the following exponential sum n=1Ne2πitnd+2πixn. \sum_{n=1}^N e^{2\pi i tn^d +2\pi i xn}\,.

Keywords

Cite

@article{arxiv.2309.11590,
  title  = {A remark on the mean value inequalities related to Waring's problem},
  author = {Xiaochun Li},
  journal= {arXiv preprint arXiv:2309.11590},
  year   = {2023}
}