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  • Brandes, Julia, et al. (author)
  • On generating functions in additive number theory, II: lower-order terms and applications to PDEs
  • 2021
  • In: Mathematische Annalen. - : Springer Science and Business Media LLC. - 0025-5831 .- 1432-1807. ; 379, s. 347-76
  • Journal article (peer-reviewed)abstract
    • We obtain asymptotics for sums of the form Sigma(p)(n=1) e(alpha(k) n(k) + alpha(1)n), involving lower order main terms. As an application, we show that for almost all alpha(2) is an element of [0, 1) one has sup(alpha 1 is an element of[0,1)) | Sigma(1 <= n <= P) e(alpha(1)(n(3) + n) + alpha(2)n(3))| << P3/4+epsilon, and that in a suitable sense this is best possible. This allows us to improve bounds for the fractal dimension of solutions to the Schrodinger and Airy equations.
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Type of publication
journal article (1)
Type of content
peer-reviewed (1)
Author/Editor
Brandes, Julia (1)
Parsell, S. T. (1)
Poulias, C. (1)
Shakan, G. (1)
Vaughan, R. C. (1)
University
University of Gothenburg (1)
Chalmers University of Technology (1)
Language
English (1)
Research subject (UKÄ/SCB)
Natural sciences (1)
Year
2021 (1)

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