Investigations on the properties of the arithmetic derivative

2011/08/24 by Niklas Dahl, Dahl, Niklas, Jonas Olsson +3
Mathematics · #11R04 #Analytic Number Theory Research #FOS: Mathematics #History and Theory of Mathematics #Mathematics and Applications #Number Theory (math.NT) #math.NT #msc:11R04

paper · pdf · doi:10.48550/arxiv.1108.4762

10 pages, no figures

arxiv created 2011/08/24 · openalex publication_date 2011/08/24 · arxiv updated 2011/08/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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