Dmitry Zhelezov

most citedImproved bounds for arithmetic progressions in product sets

1 citations · 1 across the 2 of their papers we have counts for

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2 papers

math.NT2015★ 1 cited

Improved bounds for arithmetic progressions in product sets

Dmitry Zhelezov

Let $B$ be a set of natural numbers of size $n$ . We prove that the length of the longest arithmetic progression contained in the product set $B . B = {b b^{'} ∣ b, b^{'} \in B}$ cannot…

math.NT2015

On sets with small additive doubling in product sets

Dmitry Zhelezov

Following the sum-product paradigm, we prove that for a set $B$ with polynomial growth, the product set $B . B$ cannot contain large subsets with size of order $∣ B ∣^{2}$ with small dou…