Geodesic
New bound for Roth's theorem with generalized coefficients
Discrete analysis (2022) Cet article a éte moissonné depuis la source Scholastica

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We prove the following conjecture of Shkredov and Solymosi: every subset $A \subset \mathbf{Z}^2$ such that $\sum_{a\in A\setminus\{0\}} 1/\left\|a\right\|^{2} = +\infty$ contains the three vertices of an isosceles right triangle. To do this, we adapt the proof of the recent breakthrough by Bloom and Sisask on sets without three-term arithmetic progressions, to handle more general equations of the form $T_1a_1+T_2a_2+T_3a_3 = 0$ in a finite abelian group $G$, where the $T_i$'s are automorphisms of $G$.
Publié le : 
@article{DAS_2022_a4,
     author = {C\'edric Pilatte},
     title = {New bound for {Roth's} theorem with generalized coefficients},
     journal = {Discrete analysis},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DAS_2022_a4/}
}
TY  - JOUR
AU  - Cédric Pilatte
TI  - New bound for Roth's theorem with generalized coefficients
JO  - Discrete analysis
PY  - 2022
UR  - http://geodesic.mathdoc.fr/item/DAS_2022_a4/
LA  - en
ID  - DAS_2022_a4
ER  - 
%0 Journal Article
%A Cédric Pilatte
%T New bound for Roth's theorem with generalized coefficients
%J Discrete analysis
%D 2022
%U http://geodesic.mathdoc.fr/item/DAS_2022_a4/
%G en
%F DAS_2022_a4
Cédric Pilatte. New bound for Roth's theorem with generalized coefficients. Discrete analysis (2022). http://geodesic.mathdoc.fr/item/DAS_2022_a4/