Geodesic
ON A DIAGONAL QUADRIC IN DENSE VARIABLES
Glasgow mathematical journal, Tome 56 (2014) no. 3, pp. 601-628

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DOI

We examine the solubility of a diagonal, translation invariant, quadratic equation system in arbitrary (dense) subsets $\mathcal{A}$ ⊂ Z and show quantitative bounds on the size of $\mathcal{A}$ if there are no non-trivial solutions. We use the circle method and Roth's density increment argument. Due to a restriction theory approach we can deal with equations in s ≥ 7 variables.
DOI : 10.1017/S0017089514000056
Mots-clés : Primary 11B30, Secondary 11P55, 11D09, 11L07 
KEIL, EUGEN. ON A DIAGONAL QUADRIC IN DENSE VARIABLES. Glasgow mathematical journal, Tome 56 (2014) no. 3, pp. 601-628. doi: 10.1017/S0017089514000056
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     title = {ON {A} {DIAGONAL} {QUADRIC} {IN} {DENSE} {VARIABLES}},
     journal = {Glasgow mathematical journal},
     pages = {601--628},
     year = {2014},
     volume = {56},
     number = {3},
     doi = {10.1017/S0017089514000056},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089514000056/}
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