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math.NT2020
An update on the sum-product problem
Misha Rudnev, Sophie Stevens
We improve the best known sum-product estimates over the reals. We prove that \[ \max(|A+A|,|AA|)\geq |A|^{\frac{4}{3} + \frac{2}{1167} - o(1)}\,, \] for a finite $A\subset \mathbb…
math.NT2020
Higher convexity and iterated sum sets
Brandon Hanson, Oliver Roche-Newton, Misha Rudnev
Let be a smooth real function with strictly monotone first derivatives. We show that for a finite set , with , $|2^kf(A)-(2^k-1)f(A)|\gg_k |A|^{k+1-o(1)}…