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.
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