Number Theory

    

The Prime Index Function

Authors: Theophilus Agama

In this paper we introduce the prime index function \begin{align}\iota(n)=(-1)^{\pi(n)},\nonumber \end{align} where $\pi(n)$ is the prime counting function. We study some elementary properties and theories associated with the partial sums of this function given by\begin{align}\xi(x):=\sum \limits_{n\leq x}\iota(n).\nonumber \end{align}

Comments: 7 Pages.

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Submission history

[v1] 2020-01-29 10:55:43

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