Logarithmic and absolute-value like properties of $π(x)$ with applications

Details Logarithmic and absolute-value like properties of $π(x)$ with applications Logarithmic and absolute-value like properties of $π(x)$ with applications

2011-08-09

arxiv.org/abs/1108.2020v2

Mathematics

Number Theory

11 pages. Withdrawn by the author due to a problem with Theorem 3.1, thus also invalidating all results that were based on it

Scientific paper

We derive properties of $\pi(x)$ reminiscent of those of the logarithm and
absolute value functions. Two of these properties are similar to the relations
defining the linearity of a function. Several applications of these properties
of $\pi(x)$ are also examined.

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