Geodesic
The Measure of the Set of Zeros of the Sum of a Nondegenerate Sine Series with Monotone Coefficients in the Closed Interval $[0,\pi]$
Matematičeskie zametki, Tome 103 (2018) no. 4, pp. 576-581

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Nonzero sine series with monotone coefficients tending to zero are considered. It is shown that the measure of the set of those zeros of such a series which belong to $[0,\pi]$ cannot exceed $\pi/3$. Moreover, if this value is attained, then almost all zeros belong to the closed interval $[2\pi/3,\pi]$.
Keywords: sine series, zeros of a function, measure of a set.
Mots-clés : monotone coefficients 
@article{MZM_2018_103_4_a8,
     author = {K. A. Oganesyan},
     title = {The {Measure} of the {Set} of {Zeros} of the {Sum} of a {Nondegenerate} {Sine} {Series} with {Monotone} {Coefficients} in the {Closed} {Interval} $[0,\pi]$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {576--581},
     publisher = {mathdoc},
     volume = {103},
     number = {4},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2018_103_4_a8/}
}
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K. A. Oganesyan. The Measure of the Set of Zeros of the Sum of a Nondegenerate Sine Series with Monotone Coefficients in the Closed Interval $[0,\pi]$. Matematičeskie zametki, Tome 103 (2018) no. 4, pp. 576-581. http://geodesic.mathdoc.fr/item/MZM_2018_103_4_a8/