On generating functions in additive number theory, II: lower-order terms and applications to PDEs
Artikel i vetenskaplig tidskrift, 2021

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

Chalmers, Matematiska vetenskaper, Algebra och geometri

Göteborgs universitet

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. 379 1-2 347-376

Högre-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

Mer information

Senast uppdaterat

2021-03-24