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arXiv · 1308.6680

Translation invariant quadratic forms in dense sets

Eugen Keil
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Abstract

We generalize Roth's theorem on three term arithmetic progressions to translation invariant quadratic forms in at least 17 variables. We use Fourier-analysis, restriction theory, uniformity norms and Roth's density increment method to show quantitative estimates for subsets of the integers without any non-trivial solutions.

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Eugen Keil. 2013-08-30. Translation invariant quadratic forms in dense sets. https://arxiv.org/abs/1308.6680

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