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arXiv · 1003.3780

On van der Corput property of squares

Sinisa Slijepcevic
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Abstract

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 a_0=O((log n)^{-1/3}).

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Sinisa Slijepcevic. 2010-03-19. On van der Corput property of squares. https://arxiv.org/abs/1003.3780

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