Abstract
It is shown that there exist arbitrarily large natural numbers $$N$$ and distinct nonnegative integers $$n_1,\dots,n_N$$ for which the number of zeros on $$[-\pi,\pi)$$ of the trigonometric polynomial $$\sum_{j=1}^N \cos(n_j t)$$ is $$O(N^{2/3}\log^{2/3} N)$$ .
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