Geodesic
New bound for Roth's theorem with generalized coefficients
Discrete analysis (2022)

Voir la notice de l'article provenant de la source Scholastica

arXiv
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 : 
Cédric Pilatte. New bound for Roth's theorem with generalized coefficients. Discrete analysis (2022). http://geodesic.mathdoc.fr/item/DAS_2022_a4/
@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/}
}
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