Geodesic
Counting monochromatic solutions to diagonal Diophantine equations
Discrete analysis (2021) Cet article a éte moissonné depuis la source Scholastica

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We show how to adapt the Hardy--Littlewood circle method to count monochromatic solutions to diagonal Diophantine equations. This delivers a lower bound which is optimal up to absolute constants. The method is illustrated on equations obtained by setting a diagonal quadratic form equal to a linear form. As a consequence, we determine an algebraic criterion for when such equations are partition regular. Our methods involve discrete harmonic analysis and require a number of `mixed' restriction estimates, which may be of independent interest.
Publié le : 
@article{DAS_2021_a13,
     author = {Sean Prendiville},
     title = {Counting monochromatic solutions to diagonal {Diophantine} equations},
     journal = {Discrete analysis},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DAS_2021_a13/}
}
TY  - JOUR
AU  - Sean Prendiville
TI  - Counting monochromatic solutions to diagonal Diophantine equations
JO  - Discrete analysis
PY  - 2021
UR  - http://geodesic.mathdoc.fr/item/DAS_2021_a13/
LA  - en
ID  - DAS_2021_a13
ER  - 
%0 Journal Article
%A Sean Prendiville
%T Counting monochromatic solutions to diagonal Diophantine equations
%J Discrete analysis
%D 2021
%U http://geodesic.mathdoc.fr/item/DAS_2021_a13/
%G en
%F DAS_2021_a13
Sean Prendiville. Counting monochromatic solutions to diagonal Diophantine equations. Discrete analysis (2021). http://geodesic.mathdoc.fr/item/DAS_2021_a13/