Original scientific paper

https://doi.org/10.3336/gm.45.2.05

On van der Corput property of squares

Siniša Slijepčević orcid.org/0000-0001-5600-0171 ; Department of Mathematics, University of Zagreb, Bijenička 30, 10000 Zagreb, Croatia

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).

Keywords

Sárközy theorem; recurrence; difference sets; positive definiteness; van der Corput property; Fourier analysis

Hrčak ID:

62693

URI

https://hrcak.srce.hr/62693

Publication date:

24.12.2010.

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