The fractal nature of an approximate prime counting function

TL;DR

This paper explores the fractal properties of an approximate prime counting function by combining additive approximations with Fourier basis elements, revealing complex geometric structures related to prime numbers.

Contribution

It introduces a novel fractal representation of the prime counting function using additive and Fourier basis methods, bridging number theory and fractal geometry.

Findings

Identification of fractal polygons and curves related to prime numbers

Demonstration of complex geometric structures in prime number approximations

Potential insights into prime distribution through fractal analysis

Abstract

Prime number related fractal polygons and curves are derived by combining two different aspects. One is an approximation of the prime counting function build on an additive function. The other are prime number indexed basis entities taken from the discrete or continuous Fourier basis.