Definition:Logarithmic Mean Value

Definition

Let $f: \N \to \C$ be an arithmetic function.

The logarithmic mean value of $f$ is the limit:

$\map L f = \ds \lim_{x \mathop \to \infty} \frac 1 {\ln x} \sum_{n \mathop \le x} \frac {\map f n} n$

if it exists.

Also see

• Definition:Ordinary Mean Value
• Existence of Ordinary Mean Value Implies Existence of Logarithmic Mean Value