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≥7, and in particular establish that for large k one has H(k)≤(4k−2)logk−(2log2−1)k−3.
- Vinogradov mean-value theorem
- Waring–Goldbach problem
- Weyl sums