On a diagonal quadric in dense variables

Eugen Keil

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arXiv · 1306.4524

On a diagonal quadric in dense variables

Eugen Keil

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Abstract

We examine the solubility of a diagonal, translation invariant, quadratic equation system in arbitrary (dense) subsets A \subset Z and show quantitative bounds on the size of 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 \geq 7 variables.

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Eugen Keil. 2013-08-30. On a diagonal quadric in dense variables. https://arxiv.org/abs/1306.4524

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