TY - JOUR
T1 - ON ITERATED PRODUCT SETS with SHIFTS
AU - Hanson, Brandon
AU - Roche-Newton, Oliver
AU - Zhelezov, Dmitrii
N1 - Funding Information:
Oliver Roche-Newton was partially supported by the Austrian Science Fund FWF Projects F5509 and P 30405-N32. Dmitrii Zhelezov was partially supported by the Knuth and Alice Wallenberg Foundation Program for Mathematics 2017. We thank Brendan Murphy and Endre Szemerédi for helpful conversations. We also thank the anonymous referee for several helpful comments and corrections.
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
VL - 65
SP - 831
EP - 850
JO - Mathematika
JF - Mathematika
SN - 0025-5793
IS - 4
ER -