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On Waring's problem for larger powers (2211.10380v1)
Published 18 Nov 2022 in math.NT
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 $k\ge 14$.