A+ CATEGORY SCIENTIFIC UNIT

PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

On smooth Weyl sums over biquadrates and Waring’s problem

Volume 204 / 2022

Jörg Brüdern, Trevor D. Wooley 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.

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

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image