ON ITERATED PRODUCT SETS with SHIFTS

Brandon Hanson; Oliver Roche-Newton; Dmitrii Zhelezov

doi:10.1112/S0025579319000081

ON ITERATED PRODUCT SETS with SHIFTS

Brandon Hanson
, Oliver Roche-Newton
, Dmitrii Zhelezov

Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

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 language	English (US)
Pages (from-to)	831-850
Number of pages	20
Journal	Mathematika
Volume	65
Issue number	4
DOIs	https://doi.org/10.1112/S0025579319000081
State	Published - 2019

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1112/S0025579319000081

Cite this

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title = "ON ITERATED PRODUCT SETS with SHIFTS",

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.",

author = "Brandon Hanson and Oliver Roche-Newton and Dmitrii Zhelezov",

note = "Publisher Copyright: {\textcopyright} 2019 University College London.",

year = "2019",

doi = "10.1112/S0025579319000081",

language = "English (US)",

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T1 - ON ITERATED PRODUCT SETS with SHIFTS

AU - Hanson, Brandon

AU - Roche-Newton, Oliver

AU - Zhelezov, Dmitrii

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/85065926575

UR - https://www.scopus.com/pages/publications/85065926575#tab=citedBy

U2 - 10.1112/S0025579319000081

DO - 10.1112/S0025579319000081

M3 - Article

AN - SCOPUS:85065926575

SN - 0025-5793

VL - 65

SP - 831

EP - 850

JO - Mathematika

JF - Mathematika

IS - 4

ER -

ON ITERATED PRODUCT SETS with SHIFTS

Abstract

All Science Journal Classification (ASJC) codes

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