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arXiv · 2211.10380

On Waring's problem for larger powers

Joerg Bruedern·Trevor D. Wooley
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Abstract

Let $G(k)$ denote the least number $s$ having the property that every sufficiently large natural number is the sum of at most $s$ positive integral $k$-th powers. Then for all $k\in \mathbb N$, one has \[ G(k)\le \lceil k(\log k+4.20032)\rceil . \] Our new methods improve on all bounds available hitherto when $k\ge 14$.

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Joerg Bruedern, Trevor D. Wooley. 2022-11-18. On Waring's problem for larger powers. https://arxiv.org/abs/2211.10380

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