An explicit estimate for the Barban and Vehov weights

Djamel Berkane
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 20, 2014, Number 2, Pages 35–43
Full paper (PDF, 164 Kb)

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Djamel Berkane
Department of Mathematics, University of Blida, Algeria

Abstract

We show that

    \[\sum_{1 \le n \le N} \Bigg ( \sum_{d|n} \lambda_d \Bigg )^2 / n <\!\!< \dfrac{\log N}{\log z},\]

where \lambda_{d} is a real valued arithmetic function called the Barban and Vehov weight and we give an explicit version of a Theorem of Barban and Vehov which has applications to zero-density theorems.

Keywords

  • Explicit estimates
  • Möbius function
  • Selberg sieve

AMS Classification

  • Primary: 11N37
  • Secondary: 11N35, 11N05

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Cite this paper

Berkane, D. (2014). An explicit estimate for the Barban and Vehov weights. Notes on Number Theory and Discrete Mathematics, 20(2), 35-43.

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