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

1 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 - Jan 1 2019

All Science Journal Classification (ASJC) codes

Mathematics(all)

Access to Document

10.1112/S0025579319000081

Fingerprint Dive into the research topics of 'ON ITERATED PRODUCT SETS with SHIFTS'. Together they form a unique fingerprint.

Cite this

@article{9335d74e0ffa48269c8d4dd8b5b4e9d7,

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",

year = "2019",

month = jan,

day = "1",

doi = "10.1112/S0025579319000081",

language = "English (US)",

volume = "65",

pages = "831--850",

journal = "Mathematika",

issn = "0025-5793",

publisher = "University College London",

number = "4",

}

TY - JOUR

T1 - ON ITERATED PRODUCT SETS with SHIFTS

AU - Hanson, Brandon

AU - Roche-Newton, Oliver

AU - Zhelezov, Dmitrii

PY - 2019/1/1

Y1 - 2019/1/1

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 - http://www.scopus.com/inward/record.url?scp=85065926575&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85065926575&partnerID=8YFLogxK

U2 - 10.1112/S0025579319000081

DO - 10.1112/S0025579319000081

M3 - Article

AN - SCOPUS:85065926575

VL - 65

SP - 831

EP - 850

JO - Mathematika

JF - Mathematika

SN - 0025-5793

IS - 4

ER -