Global Field Totients
Number Theory
2020-05-13 v2
Abstract
Using a remainder theorem for valuations of a field, we give a new perspective on the norm function of a global field. We define the Euler totient function of a global field and recover the essential analytical properties of the classical arithmetical function, namely the product formula. In addition, we prove the holomorphicity of the associated zeta function. As an application, we recover the analog of the mean value theorem of Erd\H{o}s, Dressler, and Bateman via the Weiner-Ikehara theorem.
Keywords
Cite
@article{arxiv.2005.04521,
title = {Global Field Totients},
author = {Santiago Arango-Piñeros and Juan Diego Rojas},
journal= {arXiv preprint arXiv:2005.04521},
year = {2020}
}