On the Waring--Goldbach problem for eighth and higher powers
Number Theory
2017-05-17 v1
Abstract
Recent progress on Vinogradov's mean value theorem has resulted in improved estimates for exponential sums of Weyl type. We apply these new estimates to obtain sharper bounds for the function in the Waring--Goldbach problem. We obtain new results for all exponents , and in particular establish that when is large, giving the first improvement on the classical result of Hua from the 1940s.
Keywords
Cite
@article{arxiv.1510.00982,
title = {On the Waring--Goldbach problem for eighth and higher powers},
author = {Angel V. Kumchev and Trevor D. Wooley},
journal= {arXiv preprint arXiv:1510.00982},
year = {2017}
}