Investigations on the properties of the arithmetic derivative
Number Theory
2011-08-25 v1
Abstract
We investigate the properties of arithmetic differentiation, an attempt to adapt the notion of differentiation to the integers by preserving the Leibniz rule, (ab)' = a'b + ab'. This has proved to be a very rich topic with many different aspects and implications to other fields of mathematics and specifically to various unproven conjectures in additive prime number theory. Our paper consists of a self-contaited introduction to the topic, along with a couple of new theorems, several of them related to arithmetic differentiation of rational numbers, a topic almost unexplored until now.
Keywords
Cite
@article{arxiv.1108.4762,
title = {Investigations on the properties of the arithmetic derivative},
author = {Niklas Dahl and Jonas Olsson and Alexander Loiko},
journal= {arXiv preprint arXiv:1108.4762},
year = {2011}
}
Comments
10 pages, no figures