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Logarithmic bounds for Roth’s theorem via almost-periodicity

Abstract:
We give a new proof of logarithmic bounds for Roth's theorem on arithmetic progressions, namely that if A⊂{1,2,…,N} is free of three-term progressions, then |A|≤N/(logN)1−o(1). Unlike previous proofs, this is almost entirely done in physical space using almost-periodicity.
Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.19086/da.7884

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Institution:
University of Oxford
Role:
Author
Publisher:
Diamond Open Access Journals
Journal:
Discrete Analysis More from this journal
Volume:
4
Publication date:
2019-05-10
Acceptance date:
2019-01-18
DOI:
EISSN:
2397-3129
Language:
English
Keywords:
Pubs id:
1193527
Local pid:
pubs:1193527
Deposit date:
2021-08-31

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