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 | |
| State | Published - Jan 1 2019 |
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All Science Journal Classification (ASJC) codes
- Mathematics(all)
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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 journal › Article
TY - JOUR
T1 - ON ITERATED PRODUCT SETS with SHIFTS
AU - Hanson, Brandon William
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
VL - 65
SP - 831
EP - 850
JO - Mathematika
JF - Mathematika
SN - 0025-5793
IS - 4
ER -