Fourier Dimension and Translation Invariant Linear Equations
Abstract
We consider a translation invariant linear equation in four variables with integer coefficients of the form: ax1 +bx2= cy1+dy2. The main result of the paper states that any set on the real line with Fourier dimension greater than 1/2 must contain a nontrivial solution of such an equation.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.