Journal article
Extremal problems for GCDs
- Abstract:
- We prove that if A ⊆ [X, 2X] and B ⊆ [Y, 2Y] are sets of integers such that gcd (a, b) ≥ D for at least δ |A| |B| pairs (a, b) ∈ A × B then |A| |B| <<ε δ−2−ε XY / D2. This is a new result even when δ =1. The proof uses ideas of Koukoulopoulos and Maynard and some additional combinatorial arguments.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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(Preview, Version of record, pdf, 286.0KB, Terms of use)
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- Publisher copy:
- 10.1017/S0963548321000092
Authors
- Publisher:
- Cambridge University Press
- Journal:
- Combinatorics, Probability and Computing More from this journal
- Volume:
- 30
- Issue:
- 6
- Pages:
- 922–929
- Publication date:
- 2021-04-08
- Acceptance date:
- 2021-03-29
- DOI:
- EISSN:
-
1469-2163
- ISSN:
-
0963-5483
- Language:
-
English
- Keywords:
- Pubs id:
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1150030
- Local pid:
-
pubs:1150030
- Deposit date:
-
2023-03-03
- ARK identifier:
Terms of use
- Copyright holder:
- Green and Walker
- Copyright date:
- 2021
- Rights statement:
- © The Author(s), 2021. Published by Cambridge University Press. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence, which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
- Licence:
- CC Attribution (CC BY)
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