Abstract
AbstractConsider a translation-invariant system of linear equationsVx= 0 of complexity one, whereVis an integerr×tmatrix. We show that ifAis a subset of the primes up toNof density at leastC(log logN)–1/25t, there exists a solutionx∈ AttoVx= 0 with distinct coordinates. This extends a quantitative result of Helfgott and de Roton for three-term arithmetic progressions, while the qualitative result is known to hold for all translation-invariant systems of finite complexity by the work of Green and Tao.
Full Text 
Sign-in/Register to access full text options
Sign-in/Register to access full text options 
Published version (
Free)
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
