English

On the Waring-Goldbach problem for seventh and higher powers

Number Theory 2017-07-31 v1

Abstract

We apply recent progress on Vinogradov's mean value theorem to improve bounds for the function H(k)H(k) in the Waring-Goldbach problem. We obtain new results for all exponents k7k \ge 7, and in particular establish that for large kk one has H(k)(4k2)logk(2log21)k3.H(k)\le (4k-2)\log k-(2\log 2-1)k-3.

Keywords

Cite

@article{arxiv.1602.08592,
  title  = {On the Waring-Goldbach problem for seventh and higher powers},
  author = {Angel V. Kumchev and Trevor D. Wooley},
  journal= {arXiv preprint arXiv:1602.08592},
  year   = {2017}
}
R2 v1 2026-06-22T12:59:08.631Z