The discretised ABC sum-product conjecture
Let α,β,γin(0,1)\alpha,\beta,\gamma in (0,1)α,β,γin(0,1) with β≤α\beta \leq \alphaβ≤α. Let A,B,C⊂[0,1]A,B,C \subset [0,1]A,B,C⊂[0,1] be δ\deltaδ-separated sets with ∣A∣≤δ−α|A| \leq \delta^{-\alpha}∣A∣≤δ−α, ∣B∣=δ−β|B|=\delta^{-\beta}∣B∣=δ−β, and…