Discrete Fourier restriction via Efficient Congruencing

Trevor D Wooley

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

9 Citations (Scopus)
342 Downloads (Pure)

Abstract

We show that whenever s > k(k + 1), then for any complex sequence (an)n∈Z, one has Z [0,1)k X |n|6X ane(α1n + . . . + αkn k ) 2s dα Xs−k(k+1)/2 X |n|6X |an| 2 s . Bounds for the constant in the associated periodic Strichartz inequality from L 2s to l 2 of the conjectured order of magnitude follow, and likewise for the constant in the discrete Fourier restriction problem from l 2 to L s 0 , where s 0 = 2s/(2s − 1). These bounds are obtained by generalising the efficient congruencing method from Vinogradov’s mean value theorem to the present setting, introducing tools of wider application into the subject.
Original languageEnglish
Pages (from-to)1342-1389
Number of pages48
JournalInternational Mathematics Research Notices
Volume2017
Issue number5
Early online date23 May 2016
DOIs
Publication statusPublished - 11 Mar 2017

Keywords

  • 42B05
  • 11L07
  • 42A16

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