Functiones et Approximatio Commentarii Mathematici

On van der Corput property of shifted primes

Siniša Slijepčević

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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.

Article information

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

Dates
First available in Project Euclid: 25 March 2013

Permanent link to this document
https://projecteuclid.org/euclid.facm/1364222828

Digital Object Identifier
doi:10.7169/facm/2013.48.1.4

Mathematical Reviews number (MathSciNet)
MR3086959

Zentralblatt MATH identifier
1329.11076

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

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

Citation

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. https://projecteuclid.org/euclid.facm/1364222828


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