Translation invariant quadratic forms in dense sets

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.

30 pages

Cited by in corpus (3)

• Additive equations in dense variables via truncated restriction estimates
• Some refinements for translation invariant quadratic forms in dense sets
• Translation invariant quadratic forms and dense sets of primes