In his famous book 'Introduction to Analytic and Probabilistic Number Theory', Gérald Tenenbaum established the following result (Theorem III.3.5):


Let $g$ be a positive multiplicative function and let $A$ and $B$ be two constants such that for all $y\geq 1,$
$$\sum\_{p\leq y} g(p) \log{p} \leq Ay \quad \textrm{ and } \quad \sum\_{p}\sum\_{\nu \geq 2} \frac{g(p^{\nu})\log{p^{\nu}}}{p^{\nu}}\leq B.$$
Then, for $x\geq 1,$
$$\frac{1}{x} \sum\_{n \leq x} g(n)\ll (A+B+1) \prod\_{p\leq x} \left(1-\frac{1}{p}+\sum\_{\nu \geq 1} \frac{g(p^{\nu})}{p^{\nu}}\right),$$
where **the implicit constant is absolute**.
Unfortunately, in the library of my university, I did not find Tenenbaum's book and I need to know the explicit value of the implicit constant in the previous result. Can someone help me?
Thanks in advance.



Implicit constant in Tenenbaum's result
In the French edition, it is said that the considered constant does not exceed $4(1+9\lambda\_{1}+\lambda\_{1}\lambda\_{2}/(2-\lambda\_{2})^2)$ where $\lambda\_{1}>0$, $0\leq \lambda\_{2}<2$ are such that $g(p^\nu)\leq\lambda\_{1}\lambda\_{2}^{\nu-1}$.


