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March 2013 On van der Corput property of shifted primes
Siniša Slijepčević
Funct. Approx. Comment. Math. 48(1): 37-50 (March 2013). DOI: 10.7169/facm/2013.48.1.4


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.


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Siniša Slijepčević. "On van der Corput property of shifted primes." Funct. Approx. Comment. Math. 48 (1) 37 - 50, March 2013.


Published: March 2013
First available in Project Euclid: 25 March 2013

zbMATH: 1329.11076
MathSciNet: MR3086959
Digital Object Identifier: 10.7169/facm/2013.48.1.4

Primary: 11P99
Secondary: 37A45

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

Rights: Copyright © 2013 Adam Mickiewicz University


Vol.48 • No. 1 • March 2013
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