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- W3037914360 abstract "Given two sets of natural numbers $mathcal{A}$ and $mathcal{B}$ of natural density $1$ we prove that their product set $mathcal{A}cdot mathcal{B}:={ab:ainmathcal{A},,binmathcal{B}}$ also has natural density $1$. On the other hand, for any $varepsilon>0$, we show there are sets $mathcal{A}$ of density $>1-varepsilon$ for which the product set $mathcal{A}cdotmathcal{A}$ has density $<varepsilon$. This answers two questions of Hegyv'{a}ri, Hennecart and Pach." @default.
- W3037914360 created "2020-07-02" @default.
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- W3037914360 date "2021-05-07" @default.
- W3037914360 modified "2023-10-15" @default.
- W3037914360 title "A note on the natural density of product sets" @default.
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- W3037914360 doi "https://doi.org/10.1112/blms.12506" @default.
- W3037914360 hasPublicationYear "2021" @default.
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