GCD sums and sum-product estimates

Thomas F. Bloom; Aled Walker

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arXiv · 1806.07849

GCD sums and sum-product estimates

Thomas F. Bloom·Aled Walker

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Abstract

In this note we prove a new estimate on so-called GCD sums (also called G\'{a}l sums), which, for certain coefficients, improves significantly over the general bound due to de la Bret\`{e}che and Tenenbaum. We use our estimate to prove new results on the equidistribution of sequences modulo 1, improving over a result of Aistleitner, Larcher, and Lewko on how the metric poissonian property relates to the notion of additive energy. In particular, we show that arbitrary subsets of the squares are metric poissonian.

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Thomas F. Bloom, Aled Walker. 2018-06-20. GCD sums and sum-product estimates. https://arxiv.org/abs/1806.07849

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