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A Half-Constant Upper Bound for Chowla's Cosine Problem
Let lambda(n) denote the infimum of -min_x sum_{a in A} cos(ax) over all sets A of n positive integers. While the classical Sidon-difference construction yields lambda(n) <= (1 + o(1))sqrt(n)/2, we construct sets achieving a leading constant of 1/2: lambda(n) <= (1/2)sqrt(n) + O(n^(1/4)sqrt(log n)),
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