Complex Network Approach to Number Theory
Abstract
In this short paper, following the most recent advances in complex network theory, a new approach to number theory with potential applications to other fields is proposed. The model by Garcia-Perez, Serrano and Boguna, introduces an algorithm which allows to create a bipartite graph of integers (with primes and composites) statistically very close to the real one. Since the algorithm is defined a priori, we can have a description of the simulated prime number distribution in terms of a known differential equation, which in general can be treated more easily. The so determined properties of the simulated distribution can give useful hints about the behavior of the real prime number distribution. In principle it could be also possible to demonstrate open questions in number theory, proven the total equivalence of the simulated and real distributions.
Cite
@article{arxiv.1409.3120,
title = {Complex Network Approach to Number Theory},
author = {Daniele Vilone},
journal= {arXiv preprint arXiv:1409.3120},
year = {2014}
}
Comments
This paper has been withdrawn by the author. Due to en error, one of the main conclusions of the paper is not supported by the calculations as indicated in the text