ON ITERATED PRODUCT SETS with SHIFTS

Brandon Hanson, Oliver Roche-Newton, Dmitrii Zhelezov

Research output: Contribution to journalArticle

Abstract

We prove that, for any finite set A ⊂ Q with AA ≤ K A and any positive integer k, the k-fold product set of the shift A + 1 satisfies the bound [equation presented]. This result is essentially optimal when K is of the order c log A, for a sufficiently small constant c = c(k). Our main tool is a multiplicative variant of the 3-constants used in harmonic analysis, applied to Dirichlet polynomials.

Original languageEnglish (US)
Pages (from-to)831-850
Number of pages20
JournalMathematika
Volume65
Issue number4
DOIs
Publication statusPublished - Jan 1 2019

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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