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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Acknowledgments
The author wishes to express gratitude to K. S. Ryutin for his interest in the paper and useful remarks. Without his careful reading, the paper stood little chance of being sent to press.
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Konyagin, S.V. On Zeros of Sums of Cosines. Math Notes 108, 538–541 (2020). https://doi.org/10.1134/S0001434620090254
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DOI: https://doi.org/10.1134/S0001434620090254