English

Translation invariant quadratic forms in dense sets

Number Theory 2013-09-02 v1

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.

Keywords

Cite

@article{arxiv.1308.6680,
  title  = {Translation invariant quadratic forms in dense sets},
  author = {Eugen Keil},
  journal= {arXiv preprint arXiv:1308.6680},
  year   = {2013}
}

Comments

30 pages

R2 v1 2026-06-22T01:17:49.397Z