Functiones et Approximatio Commentarii Mathematici

Explicit expression of a Barban & Vehov Theorem

Mohamed Haye Betah

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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

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

First available in Project Euclid: 26 June 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11N37: Asymptotic results on arithmetic functions 11Y35: Analytic computations
Secondary: 11A25: Arithmetic functions; related numbers; inversion formulas

explicit estimates Möbius function


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.

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