On smooth Weyl sums over biquadrates and Waring’s problem
Volume 204 / 2022
Acta Arithmetica 204 (2022), 19-40
MSC: Primary 11P05; Secondary 11L15, 11P55.
DOI: 10.4064/aa210910-6-4
Published online: 12 May 2022
Abstract
We provide estimates for $s$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 $n\equiv r$ (mod $16$), with $1\le r\le 12$, can be written as a sum of $12$ biquadrates of smooth numbers.
