Geodesic
On Zeros of Sums of Cosines
Matematičeskie zametki, Tome 108 (2020) no. 4, pp. 547-551.

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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  $O(N^{2/3}\log^{2/3} N)$.
Keywords: trigonometric polynomials, Dirichlet kernel. 
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     author = {S. V. Konyagin},
     title = {On {Zeros} of {Sums} of {Cosines}},
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S. V. Konyagin. On Zeros of Sums of Cosines. Matematičeskie zametki, Tome 108 (2020) no. 4, pp. 547-551. http://geodesic.mathdoc.fr/item/MZM_2020_108_4_a5/

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