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arXiv · 2211.10387

Partitio Numerorum: sums of a prime and a number of $k$-th powers

Joerg Bruedern·Trevor D. Wooley
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Abstract

Let $k$ be a natural number and let $c=2.134693\ldots$ be the unique real solution of the equation $2c=2+\log (5c-1)$ in $[1,\infty)$. Then, when $s\ge ck+4$, we establish an asymptotic lower bound of the expected order of magnitude for the number of representations of a large positive integer as the sum of one prime and $s$ positive integral $k$-th powers.

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Joerg Bruedern, Trevor D. Wooley. 2022-11-18. Partitio Numerorum: sums of a prime and a number of $k$-th powers. https://arxiv.org/abs/2211.10387

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