Vinogradov's mean value theorem via efficient congruencing
Number Theory
2012-08-13 v1
Abstract
We obtain estimates for Vinogradov's integral which for the first time approach those conjectured to be the best possible. Several applications of these new bounds are provided. In particular, the conjectured asymptotic formula in Waring's problem holds for sums of s kth powers of natural numbers whenever s is at least 2k^2+2k-3.
Cite
@article{arxiv.1101.0574,
title = {Vinogradov's mean value theorem via efficient congruencing},
author = {Trevor D. Wooley},
journal= {arXiv preprint arXiv:1101.0574},
year = {2012}
}