arxiv: 1602.08592 · v1 · pith:RRTN742Inew · submitted 2016-02-27 · 🧮 math.NT

On the Waring-Goldbach problem for seventh and higher powers

Angel V. Kumchev , Trevor D. Wooley This is my paper

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keywords problemwaring-goldbachapplyboundsestablishexponentsfunctionhigher

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

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On the Waring-Goldbach problem for seventh and higher powers

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