On smooth Weyl sums over biquadrates and Waring’s problem

Jörg Brüdern, Trevor D. Wooley Acta Arithmetica 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.

Authors

  • Jörg BrüdernMathematisches Institut
    Bunsenstrasse 3–5
    D-37073 Göttingen, Germany
    e-mail
  • Trevor D. WooleyDepartment of Mathematics
    Purdue University
    150 N. University Street
    West Lafayette, IN 47907-2067, USA
    e-mail

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