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GCD sums and sum-product estimates

Accepted version
Peer-reviewed

Type

Article

Change log

Authors

Bloom, Thomas F 

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

Volume Title

235

Publisher

Springer Nature

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.