On van der Corput property of squares

2010/03/19 by Sinisa Slijepcevic, Slijepcevic, Sinisa
Mathematics · #11P99 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11P99

paper · pdf · doi:10.48550/arxiv.1003.3780

arxiv created 2010/03/19 · arxiv updated 2010/03/22

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 a₀=O((log n)^-1/3).

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