On van der Corput property of squares
Number Theory
2010-03-22 v1
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}).
Keywords
Cite
@article{arxiv.1003.3780,
title = {On van der Corput property of squares},
author = {Sinisa Slijepcevic},
journal= {arXiv preprint arXiv:1003.3780},
year = {2010}
}