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 $p-1$, $p\leq n$, and a small free coefficient $a_{0}=O((\log n)^{-1+o(1)})$. This implies the same bound for the intersective property of the set $p-1$, and also bounds for several properties related to uniform distribution of related sets.
Citation
Siniša Slijepčević. "On van der Corput property of shifted primes." Funct. Approx. Comment. Math. 48 (1) 37 - 50, March 2013. https://doi.org/10.7169/facm/2013.48.1.4
Information