TY - JOUR
T1 - ON ITERATED PRODUCT SETS with SHIFTS
AU - Hanson, Brandon
AU - Roche-Newton, Oliver
AU - Zhelezov, Dmitrii
N1 - Publisher Copyright:
© 2019 University College London.
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.
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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 -