A corrected version of Costello's conjecture holds for multilinear polynomials with optimal exponent 1, complex quadratics get a 13/24 power saving, and the original conjecture is false for degree at least 3.
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Algebraic aspects of the polynomial Littlewood-Offord problem
A corrected version of Costello's conjecture holds for multilinear polynomials with optimal exponent 1, complex quadratics get a 13/24 power saving, and the original conjecture is false for degree at least 3.