Some refinements for translation invariant quadratic forms in dense sets

2014/08/07 by Eugen Keil, Keil, Eugen
Mathematics · #11B30 (Primary) 11P55 #11D09 (Secondary) #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11B30 #msc:11D09 #msc:11P55

paper · pdf · doi:10.48550/arxiv.1408.1535

Preprint, 12 pages

arxiv created 2014/08/07 · arxiv updated 2014/08/08

Abstract

We improve the result of our previous paper on translation invariant quadratic forms in two special cases. We reduce the density bound |A|/N = O((loglog N)^-c) to |A|/N = O((log N)^-c) for most quadratic forms and handle almost diagonal equations in s ≥ 6 variables instead of s ≥ 8.

Related

• Translation invariant quadratic forms in dense sets
• On a diagonal quadric in dense variables
• Translation invariant quadratic forms and dense sets of primes
• Logarithmic bounds for translation-invariant equations in squares
• Effective density for inhomogeneous quadratic forms II: fixed forms and generic shifts