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Mat. Zametki, 2020, Volume 108, Issue 4, Pages 547–551 (Mi mz12828)  

On Zeros of Sums of Cosines

S. V. Konyagin

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: It is shown that there exist arbitrarily large natural numbers $N$ and distinct nonnegative integers $n_1,…,n_N$ 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.

DOI: https://doi.org/10.4213/mzm12828

Full text: PDF file (397 kB)
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English version:
Mathematical Notes, 2020, 108:4, 538–541

Bibliographic databases:

UDC: 517.518.4
Received: 29.04.2020

Citation: S. V. Konyagin, “On Zeros of Sums of Cosines”, Mat. Zametki, 108:4 (2020), 547–551; Math. Notes, 108:4 (2020), 538–541

Citation in format AMSBIB
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