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June 2019 Explicit expression of a Barban & Vehov Theorem
Mohamed Haye Betah
Funct. Approx. Comment. Math. 60(2): 177-193 (June 2019). DOI: 10.7169/facm/1712

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.

Citation

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Mohamed Haye Betah. "Explicit expression of a Barban & Vehov Theorem." Funct. Approx. Comment. Math. 60 (2) 177 - 193, June 2019. https://doi.org/10.7169/facm/1712

Information

Published: June 2019
First available in Project Euclid: 26 June 2018

zbMATH: 07068530
MathSciNet: MR3964259
Digital Object Identifier: 10.7169/facm/1712

Subjects:
Primary: 11N37 , 11Y35
Secondary: 11A25

Keywords: explicit estimates , Möbius function

Rights: Copyright © 2019 Adam Mickiewicz University

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Vol.60 • No. 2 • June 2019
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