On van der Corput property of shifted primes
Number Theory
2011-12-14 v2
Abstract
We prove that the upper bound for the van der Corput property of the set of shifted primes is O((log n)^{-1+o(1)}), giving an answer to a problem considered by Ruzsa and Montgomery for the set of shifted primes p-1. We construct normed non-negative valued cosine polynomials with the spectrum in the set p-1, p<=n, and a small free coefficient a_0=O((log n)^{-1+o(1)}). This implies the same bound for the Poincar\'e property of the set p-1, and also bounds for several properties related to uniform distribution of related sets.
Keywords
Cite
@article{arxiv.1003.3783,
title = {On van der Corput property of shifted primes},
author = {Sinisa Slijepcevic},
journal= {arXiv preprint arXiv:1003.3783},
year = {2011}
}