## Functiones et Approximatio Commentarii Mathematici

### Explicit expression of a Barban & Vehov Theorem

Mohamed Haye Betah

#### Abstract

We prove that $$S=\sum_{n \leq N} {(\sum\limits_{d|n}\lambda_d^{(1)})^2}/{n}\leq 166 \frac{\log N}{\log z}$$ where $N \geq z \geq 100$, where the $\lambda_d^{(1)}$ is the weight introduced by Barban & Vehov in 1968, namely $$\lambda_d^{(1)}= \begin{cases} \mu(d) & \text{when d \leq z} ,\\ \mu(d)\frac{\log({z^2}/{d})}{\log z} & \text{when z< d \leq z^2}, \\ 0 & \text{when z^2<d,} \end{cases}$$ where $\mu$ is the Möbius function.

#### Article information

Source
Funct. Approx. Comment. Math., Volume 60, Number 2 (2019), 177-193.

Dates
First available in Project Euclid: 26 June 2018

https://projecteuclid.org/euclid.facm/1529978432

Digital Object Identifier
doi:10.7169/facm/1712

Mathematical Reviews number (MathSciNet)
MR3964259

Zentralblatt MATH identifier
07068530

#### Citation

Betah, Mohamed Haye. Explicit expression of a Barban &amp; Vehov Theorem. Funct. Approx. Comment. Math. 60 (2019), no. 2, 177--193. doi:10.7169/facm/1712. https://projecteuclid.org/euclid.facm/1529978432

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