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.
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