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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.
Research in the Mathematical Sciences – Springer Journals
Published: Jul 13, 2020
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