Functiones et Approximatio Commentarii Mathematici

On van der Corput property of shifted primes

Siniša Slijepčević

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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.

Article information

Funct. Approx. Comment. Math., Volume 48, Number 1 (2013), 37-50.

First available in Project Euclid: 25 March 2013

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Zentralblatt MATH identifier

Primary: 11P99: None of the above, but in this section
Secondary: 37A45: Relations with number theory and harmonic analysis [See also 11Kxx]

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


Slijepčević, Siniša. On van der Corput property of shifted primes. Funct. Approx. Comment. Math. 48 (2013), no. 1, 37--50. doi:10.7169/facm/2013.48.1.4.

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