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Logarithmic bounds for Roth's theorem via almost-periodicity
Discrete analysis (2019) Cet article a éte moissonné depuis la source Scholastica

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We give a new proof of logarithmic bounds for Roth's theorem on arithmetic progressions, namely that if $A \subset \{1,2,\ldots,N\}$ is free of three-term progressions, then $\lvert A\rvert \leq N/(\log N)^{1-o(1)}$. Unlike previous proofs, this is almost entirely done in physical space using almost-periodicity.
Publié le : 
@article{DAS_2019_a16,
     author = {Thomas F. Bloom and Olof Sisask},
     title = {Logarithmic bounds for {Roth's} theorem via almost-periodicity},
     journal = {Discrete analysis},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DAS_2019_a16/}
}
TY  - JOUR
AU  - Thomas F. Bloom
AU  - Olof Sisask
TI  - Logarithmic bounds for Roth's theorem via almost-periodicity
JO  - Discrete analysis
PY  - 2019
UR  - http://geodesic.mathdoc.fr/item/DAS_2019_a16/
LA  - en
ID  - DAS_2019_a16
ER  - 
%0 Journal Article
%A Thomas F. Bloom
%A Olof Sisask
%T Logarithmic bounds for Roth's theorem via almost-periodicity
%J Discrete analysis
%D 2019
%U http://geodesic.mathdoc.fr/item/DAS_2019_a16/
%G en
%F DAS_2019_a16
Thomas F. Bloom; Olof Sisask. Logarithmic bounds for Roth's theorem via almost-periodicity. Discrete analysis (2019). http://geodesic.mathdoc.fr/item/DAS_2019_a16/