Restriction estimates of ε -removal type for k-th powers and paraboloids

Kevin Henriot, Kevin Hughes*

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

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Abstract

We obtain restriction estimates of ε-removal type for the set of k-th powers of integers, and for discrete d-dimensional surfaces of the form {(n1,⋯,nd,n1k+⋯+ndk):|n1|,⋯,|nd|⩽N},which we term ‘k-paraboloids’. For these surfaces, we obtain a satisfying range of exponents for large values of d, k. We also obtain estimates of ε-removal type in the full supercritical range for k-th powers and for k-paraboloids of dimension d< k(k- 2). We rely on a variety of techniques in discrete harmonic analysis originating in Bourgain’s works on the restriction theory of the squares and the discrete parabola.

Original languageEnglish
Pages (from-to)963-998
Number of pages36
JournalMathematische Annalen
Volume372
Issue number3-4
Early online date23 Feb 2018
DOIs
Publication statusPublished - Dec 2018

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