GCD sums and sum-product estimates

In this note we prove a new estimate on so-called GCD sums (also called Gál sums), which, for certain coefficients, improves significantly over the general bound due to de la Bretèche and Tenenbaum. We use our estimate to prove new results on the equidistribution of sequences modulo 1, improving ove...

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Bibliographic Details
Published inIsrael journal of mathematics Vol. 235; no. 1; pp. 1 - 11
Main Authors Bloom, Thomas F., Walker, Aled
Format Journal Article
LanguageEnglish
Published Jerusalem The Hebrew University Magnes Press 2020
Springer Nature B.V
Subjects
Algebra
Analysis
Applications of Mathematics
Group Theory and Generalizations
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Sums
Theoretical
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Summary:In this note we prove a new estimate on so-called GCD sums (also called Gál sums), which, for certain coefficients, improves significantly over the general bound due to de la Bretèche 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.
ISSN:0021-2172
1565-8511
DOI:10.1007/s11856-019-1932-0