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math.MG2020★ 1 cited
Dimension-expanding polynomials and the discretized Elekes-Rónyai theorem
Orit E. Raz, Joshua Zahl
We characterize when bivariate real analytic functions are "dimension expanding" when applied to a Cartesian product. If is a bivariate real analytic function that is not local…
math.MG2017★ 23 cited
Breaking the 3/2 barrier for unit distances in three dimensions
Joshua Zahl
We prove that every set of points in spans unit distances. This is an improvement over the previous bound of . A key ingredient in…