On generating functions in additive number theory, II: lower-order terms and applications to PDEs

J. Brandes, S. T. Parsell, C. Poulias, G. Shakan, R. C. Vaughan

Research output: Contribution to journalArticlepeer-review

Abstract

We obtain asymptotics for sums of the form ∑n=1Pe(αknk+α1n),involving lower order main terms. As an application, we show that for almost all α2∈ [0 , 1) one has supα1∈[0,1)|∑1≤n≤Pe(α1(n3+n)+α2n3)|≪P3/4+ε,and that in a suitable sense this is best possible. This allows us to improve bounds for the fractal dimension of solutions to the Schrödinger and Airy equations.

Original languageEnglish (US)
Pages (from-to)347-376
Number of pages30
JournalMathematische Annalen
Volume379
Issue number1-2
DOIs
StatePublished - Feb 2021

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Fingerprint Dive into the research topics of 'On generating functions in additive number theory, II: lower-order terms and applications to PDEs'. Together they form a unique fingerprint.

Cite this