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.
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}
}