Journal article
GCD sums and sum-product estimates
- 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.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
Actions
Access Document
- Files:
-
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(Preview, Accepted manuscript, 248.7KB, Terms of use)
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- Publisher copy:
- 10.1007/s11856-019-1932-0
Authors
- Publisher:
- Springer
- Journal:
- Israel Journal of Mathematics More from this journal
- Volume:
- 235
- Pages:
- 1-11
- Publication date:
- 2019-10-07
- Acceptance date:
- 2019-01-10
- DOI:
- EISSN:
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1565-8511
- ISSN:
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0021-2172
- Language:
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English
- Keywords:
- Pubs id:
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1193528
- Local pid:
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pubs:1193528
- Deposit date:
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2021-08-31
Terms of use
- Copyright holder:
- The Hebrew University of Jerusalem
- Copyright date:
- 2019
- Rights statement:
- Copyright © 2019, The Hebrew University of Jerusalem
- Notes:
-
This is the accepted manuscript version of the article. The final version is available from Springer at https://doi.org/10.1007/s11856-019-1932-0
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