On a diagonal quadric in dense variables

2013/06/19 by Eugen Keil, Keil, Eugen
Mathematics · #11B30 (Primary) 11P55 #11D09 #11L07 (Secondary) #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11B30 #msc:11D09 #msc:11L07 #msc:11P55

paper · pdf · doi:10.48550/arxiv.1306.4524

24 pages

arxiv created 2013/08/30 · arxiv updated 2013/09/02

Abstract

We examine the solubility of a diagonal, translation invariant, quadratic equation system in arbitrary (dense) subsets A ⊂ 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 ≥ 7 variables.

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