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On the Waring-Goldbach problem for seventh and higher powers

Research paper by Angel V. Kumchev, Trevor D. Wooley

Indexed on: 27 Feb '16Published on: 27 Feb '16Published in: Mathematics - Number Theory



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 \[H(k)\le (4k-2)\log k-(2\log 2-1)k-3.\]