On smooth Weyl sums over biquadrates and Waring's problem

Joerg Bruedern; Trevor D. Wooley

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arXiv · 2110.04348

On smooth Weyl sums over biquadrates and Waring's problem

Joerg Bruedern·Trevor D. Wooley

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Abstract

We provide estimates for $s^{\rm th}$ moments of biquadratic smooth Weyl sums, when $10\le s\le 12$, by enhancing the second author's iterative method that delivers estimates beyond the classical convexity barrier. As a consequence, all sufficiently large integers $n$ satisfying $n\equiv r\pmod{16}$, with $1\le r\le 12$, can be written as a sum of $12$ biquadrates of smooth numbers.

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Joerg Bruedern, Trevor D. Wooley. 2021-10-08. On smooth Weyl sums over biquadrates and Waring's problem. https://arxiv.org/abs/2110.04348

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