On a question of Sárközy on gaps of product sequen

Authors: Javier Cilleruelo Thái Hoàng Lê

Publish Date: 2010/10/31

Volume: 179, Issue: 1, Pages: 285-295

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Abstract

Motivated by a question of Sárközy we study the gaps in the product sequence B = A · A = b 1 b 2 … of all products a i a j with a i a j ∈ A when A has upper Banach density α 0 We prove that there are infinitely many gaps b n+1 − b n ≪ α −3 and that for t ≥ 2 there are infinitely many tgaps b n+t − b n ≪ t 2 α −4 Furthermore we prove that these estimates are best possible

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