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- W3100573305 abstract "We prove that, for any finite set $A subset mathbb Q$ with $|AA| leq K|A|$ and any positive integer $k$, the $k$-fold product set of the shift $A+1$ satisfies the bound $$| {(a_1+1)(a_2+1) cdots (a_k+1) : a_i in A }| geq frac{|A|^k}{(8k^4)^{kK}}. $$ This result is essentially optimal when $K$ is of the order $clog|A|$, for a sufficiently small constant $c=c(k)$. Our main tool is a multiplicative variant of the $Lambda$-constants used in harmonic analysis, applied to Dirichlet polynomials." @default.
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- W3100573305 date "2019-01-01" @default.
- W3100573305 modified "2023-10-17" @default.
- W3100573305 title "ON ITERATED PRODUCT SETS WITH SHIFTS" @default.
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- W3100573305 doi "https://doi.org/10.1112/s0025579319000081" @default.
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