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Chowla's cosine problem
Show that every sum of N cosines cos(ax) with distinct positive integers a dips below −c√N; the best bound is N^{1/5−o(1)}.
Update from the catalog #1
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Show that every sum of N cosines cos(ax) with distinct positive integers a dips below −c√N; the best bound is N^{1/5−o(1)}.