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- W2108353757 abstract "We show that any subset of the squares of positive relative upper density contains non-trivial solutions to a translation-invariant linear equation in five or more variables, with explicit quantitative bounds. As a consequence, we establish the partition regularity of any diagonal quadric in five or more variables whose coefficients sum to zero. Unlike previous approaches, which are limited to equations in seven or more variables, we employ transference technology of Green to import bounds from the linear setting." @default.
- W2108353757 created "2016-06-24" @default.
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- W2108353757 date "2015-10-01" @default.
- W2108353757 modified "2023-09-27" @default.
- W2108353757 title "A transference approach to a Roth-type theorem in the squares" @default.
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