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
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Authors and affiliations

Djamel Berkane
Department of Mathematics, University of Blida, Algeria


We show that
\sum_{1\leq n\leq N}\Big(\sum_{\substack{d\mid n}}\lambda_{d}\Big)^2/n\ll \dfrac{\log N}{\log z},$$ where $\lambda_{d}
where λd 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.


  • 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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