Functiones et Approximatio Commentarii Mathematici

Sur les chiffres des nombres premiers translatés

Najib Ouled Azaiez, Mohamed Mkaouar, and Jörg M. Thuswaldner

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Abstract

The aim of this work is to prove new results on a class of digital functions with special emphasis on shifted primes as arguments. Our method lies on the estimate of exponential sums of the form $\sum_{n\leq x}\Lambda (n)\exp(2i\pi f(n+c_n)+\beta n)$ where $f$ a digital function, $\mathbf{c}=(c_n)$ is an almost-periodic sequence in $ \mathbb{Z}$ and $\beta $ is a real parameter, which extend the works of Mauduit-Rivat \cite{mr1} and Martin-Mauduit-Rivat \cite{mmr} to the case of the shifted prime numbers satisfying a digital constraint.

Article information

Source
Funct. Approx. Comment. Math., Volume 51, Number 2 (2014), 237-267.

Dates
First available in Project Euclid: 26 November 2014

Permanent link to this document
https://projecteuclid.org/euclid.facm/1417010853

Digital Object Identifier
doi:10.7169/facm/2014.51.2.2

Mathematical Reviews number (MathSciNet)
MR3282627

Zentralblatt MATH identifier
1353.11012

Subjects
Primary: 11A63: Radix representation; digital problems {For metric results, see 11K16} 11L03: Trigonometric and exponential sums, general 11N05: Distribution of primes
Secondary: 11L20: Sums over primes 11N60: Distribution functions associated with additive and positive multiplicative functions

Keywords
exponential sums shifted primes digital function

Citation

Mkaouar, Mohamed; Azaiez, Najib Ouled; Thuswaldner, Jörg M. Sur les chiffres des nombres premiers translatés. Funct. Approx. Comment. Math. 51 (2014), no. 2, 237--267. doi:10.7169/facm/2014.51.2.2. https://projecteuclid.org/euclid.facm/1417010853


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