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Quotients of Dense Subsets of Integers
and Short Distances between Product Elements
Yu. N. Shteinikov Scientific Research Institute for System Analysis of the Russian Academy of Sciences, Moscow
Abstract:
The lower bound
on the set of quotients of two subsets $A$,
$B$
from finite intervals of natural numbers
with positive density is refined.
This bound yields
an estimate of short distances between the elements of the product
of these two sets.
In this paper, we borrow problems,
approaches, and arguments proposed in [5] of J. Cilleruelo, D. S. Ramana, and O. Ramaré.
Keywords:
divisibility, products, quotients, distances.
Received: 19.03.2021 Revised: 20.07.2021
Citation:
Yu. N. Shteinikov, “Quotients of Dense Subsets of Integers
and Short Distances between Product Elements”, Mat. Zametki, 111:1 (2022), 117–124; Math. Notes, 111:1 (2022), 132–138
Linking options:
https://www.mathnet.ru/eng/mzm13075https://doi.org/10.4213/mzm13075 https://www.mathnet.ru/eng/mzm/v111/i1/p117
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Abstract page: | 181 | Full-text PDF : | 25 | References: | 39 | First page: | 11 |
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