GCD sums and sum-product estimates
Accepted version
Peer-reviewed
Repository URI
Repository DOI
Change log
Authors
Bloom, Thomas F
Walker, Aled https://orcid.org/0000-0002-9879-988X
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.
Description
Keywords
math.NT, math.NT
Journal Title
Israel Journal of Mathematics
Conference Name
Journal ISSN
0021-2172
1565-8511
1565-8511
Volume Title
235
Publisher
Springer Nature
Publisher DOI
Rights
All rights reserved
Sponsorship
I did this paper between the end of my DPhil in Oxford and the beginning of the Junior Research Fellowship in Cambridge.