ON ITERATED PRODUCT SETS with SHIFTS

Brandon William 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
StatePublished - Jan 1 2019

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Harmonic Analysis
Dirichlet
Finite Set
Multiplicative
Fold
Polynomial
Integer

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Hanson, Brandon William ; Roche-Newton, Oliver ; Zhelezov, Dmitrii. / ON ITERATED PRODUCT SETS with SHIFTS. In: Mathematika. 2019 ; Vol. 65, No. 4. pp. 831-850.
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Hanson, BW, Roche-Newton, O & Zhelezov, D 2019, 'ON ITERATED PRODUCT SETS with SHIFTS', Mathematika, vol. 65, no. 4, pp. 831-850. https://doi.org/10.1112/S0025579319000081

ON ITERATED PRODUCT SETS with SHIFTS. / Hanson, Brandon William; Roche-Newton, Oliver; Zhelezov, Dmitrii.

In: Mathematika, Vol. 65, No. 4, 01.01.2019, p. 831-850.

Research output: Contribution to journalArticle

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