On the Waring-Goldbach problem for seventh and higher powers

Abstract

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

References in corpus (1)

• Proof of the main conjecture in Vinogradov's mean value theorem for degrees higher than three