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dc.contributor.authorBloom, Thomas F
dc.contributor.authorWalker, Aled
dc.date.accessioned2019-04-16T23:30:53Z
dc.date.available2019-04-16T23:30:53Z
dc.date.issued2020
dc.identifier.issn0021-2172
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/291730
dc.description.abstractIn 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.
dc.description.sponsorshipI did this paper between the end of my DPhil in Oxford and the beginning of the Junior Research Fellowship in Cambridge.
dc.publisherSpringer Nature
dc.rightsAll rights reserved
dc.titleGCD sums and sum-product estimates
dc.typeArticle
prism.endingPage11
prism.publicationNameIsrael Journal of Mathematics
prism.startingPage1
prism.volume235
dc.identifier.doi10.17863/CAM.38890
dcterms.dateAccepted2019-01-06
rioxxterms.versionofrecord10.1007/s11856-019-1932-0
rioxxterms.versionAM
rioxxterms.licenseref.urihttp://www.rioxx.net/licenses/all-rights-reserved
rioxxterms.licenseref.startdate2019-01-06
dc.contributor.orcidWalker, Aled [0000-0002-9879-988X]
dc.identifier.eissn1565-8511
rioxxterms.typeJournal Article/Review
cam.issuedOnline2019-10-07
cam.orpheus.successThu Jan 30 10:46:20 GMT 2020 - Embargo updated
rioxxterms.freetoread.startdate2020-01-01


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