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The global field Euler function

The global field Euler function We define the Euler function of a global field and recover the fundamental properties of the classical arithmetical function. In addition, we prove the holomorphicity of the associated zeta function. As an application, we recover analogs of the mean value theorems of Mertens and Erdős–Dressler–Bateman. The exposition is aimed at non-experts in arithmetic statistics, with the intention of providing insight toward the generalization of arithmetical functions to other contexts within arithmetic topology. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Research in the Mathematical Sciences Springer Journals

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References (16)

Publisher
Springer Journals
Copyright
Copyright © Springer Nature Switzerland AG 2020
eISSN
2197-9847
DOI
10.1007/s40687-020-00218-3
Publisher site
See Article on Publisher Site

Abstract

We define the Euler function of a global field and recover the fundamental properties of the classical arithmetical function. In addition, we prove the holomorphicity of the associated zeta function. As an application, we recover analogs of the mean value theorems of Mertens and Erdős–Dressler–Bateman. The exposition is aimed at non-experts in arithmetic statistics, with the intention of providing insight toward the generalization of arithmetical functions to other contexts within arithmetic topology.

Journal

Research in the Mathematical SciencesSpringer Journals

Published: Jul 13, 2020

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