English

On a diagonal quadric in dense variables

Number Theory 2013-09-02 v2

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.

Keywords

Cite

@article{arxiv.1306.4524,
  title  = {On a diagonal quadric in dense variables},
  author = {Eugen Keil},
  journal= {arXiv preprint arXiv:1306.4524},
  year   = {2013}
}

Comments

24 pages

R2 v1 2026-06-22T00:36:46.523Z