On generating functions in additive number theory, II: lower-order terms and applications to PDEs
Artikel i vetenskaplig tidskrift, 2020
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.
Författare
Julia Brandes
Göteborgs universitet
Chalmers, Matematiska vetenskaper, Algebra och geometri
S. T. Parsell
West Chester University
C. Poulias
University of Bristol
G. Shakan
University of Oxford
R. C. Vaughan
Pennsylvania State University
Mathematische Annalen
0025-5831 (ISSN) 1432-1807 (eISSN)
Vol. In PressHögre-dimensionella strukturer på hyperytor
Vetenskapsrådet (VR), 2018-01-01 -- 2021-12-01.
Ämneskategorier
Beräkningsmatematik
Diskret matematik
Matematisk analys
DOI
10.1007/s00208-020-02107-0