Pseudodifferential arithmetic and the Riemann hypothesis: reminders

TL;DR

This paper revisits and expands on previous work linking pseudodifferential arithmetic to the Riemann hypothesis, providing a detailed, self-contained overview of foundational concepts necessary for the conjecture's proof.

Contribution

It offers a comprehensive, self-contained exposition of the preliminary ideas related to pseudodifferential arithmetic and its connection to the Riemann hypothesis, enhancing clarity and accessibility.

Findings

Clarified foundational concepts in pseudodifferential arithmetic

Provided a self-contained overview of necessary background

Set the stage for a potential proof of the Riemann hypothesis

Abstract

The present preprint completes the arXiv preprint #2202.11652, entitled "Pseudodifferential arithmetic and the Riemann hypothesis", devoted to a proof of the conjecture. The first 4 pages of that preprint were devoted to a set of necessary reminders, given in a very concise way: we here give a self-contained, fully developed, version of this part.