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On van der Corput property of squares
2010
Glasnik Matematicki - Serija III
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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 2010 Mathematics Subject Classification. 11P99, 37A45.
doi:10.3336/gm.45.2.05
fatcat:cpv6vrk42je6xpp7es5nsp6lxm