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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… Click to show full abstract
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.
Keywords:
product estimates;
sums sum;
sum product;
gcd sums
Journal Title: Israel Journal of Mathematics
Year Published: 2019
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Journal Title: Israel Journal of Mathematics
Year Published: 2019
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!