Perturbations of Weyl sums

Trevor D Wooley

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

8 Citations (Scopus)
198 Downloads (Pure)

Abstract

Write fk(α;X)=∑x⩽Xe(α1x+⋯+αkxk) (k⩾3). We show that there is a set B⊆[0,1)k−2 of full measure with the property that whenever (α2,…,αk−1)∈B and X is sufficiently large, then sup(α1,αk)∈[0,1)2|fk(α;X)|⩽X1/2+δk, where δk=min{1330,42k−1}. For k⩾5, this improves on work of Flaminio and Forni, in which a Diophantine condition is imposed on αk, and the exponent of X is 1−2/(3k(k−1)).
Original languageEnglish
Pages (from-to)2632-2646
Number of pages15
JournalInternational Mathematics Research Notices
Volume2016
Issue number9
Early online date24 Jul 2015
DOIs
Publication statusPublished - 10 May 2016

Bibliographical note

Preprint available at arXiv:1503.00294

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