English

Near-optimal mean value estimates for multidimensional Weyl sums

Number Theory 2021-08-03 v1

Abstract

We obtain sharp estimates for multidimensional generalisations of Vinogradov's mean value theorem for arbitrary translation-dilation invariant systems, achieving constraints on the number of variables approaching those conjectured to be the best possible. Several applications of our bounds are discussed.

Keywords

Cite

@article{arxiv.1205.6331,
  title  = {Near-optimal mean value estimates for multidimensional Weyl sums},
  author = {Scott T. Parsell and Sean M. Prendiville and Trevor D. Wooley},
  journal= {arXiv preprint arXiv:1205.6331},
  year   = {2021}
}
R2 v1 2026-06-21T21:10:49.478Z