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) |
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Pages (from-to) | 831-850 |
Number of pages | 20 |
Journal | Mathematika |
Volume | 65 |
Issue number | 4 |
DOIs | |
State | Published - Jan 1 2019 |
All Science Journal Classification (ASJC) codes
- Mathematics(all)