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arXiv · 2411.06302

Fourier Dimension and Translation Invariant Linear Equations

Angel D. Cruz
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Abstract

We consider a translation invariant linear equation in four variables with integer coefficients of the form: $ax_1 +bx_2= cy_1+dy_2$. 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.

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Angel D. Cruz. 2024-11-09. Fourier Dimension and Translation Invariant Linear Equations. https://arxiv.org/abs/2411.06302

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