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On van der Corput property of squares (CROSBI ID 171078)
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Slijepčević, Siniša
On van der Corput property of squares // Glasnik matematički, 45 (2010), 2; 357-372
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Slijepčević, Siniša
engleski
On van der Corput property of squares
We prove that the upper bound for the van der Corput property of the set of perfect squares is O((log n)-1/3), giving an answer to a problem considered by Ruzsa and Montgomery. We do it by constructing non-negative valued, normed trigonometric polynomials with spectrum in the set of perfect squares not exceeding n, and a small free coefficient a0 = O((log n)-1/3).
Sárközy theorem; recurrence; difference sets; positive definiteness; van der Corput property; Fourier analysis
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