Note on the Riemann HypothesisEasyChair Preprint 7520, version historyVersion  Date  Pages  Version notes 

1  March 5, 2022  7   2  March 16, 2022  4   3  March 17, 2022  4   4  March 24, 2022  4  We finally conclude with a complete proof of the Riemann Hypothesis  5  April 3, 2022  8  Improved some minor details (not errors, because the previous version is correct).  6  April 5, 2022  8  There seems to be a major problem in Theorem 2.3 since the series on the LHS is divergent. This was fixed.  7  April 18, 2022  8  Improved some minor details: the abstract was changed.  8  April 20, 2022  8  Fixed a wrong reference and abstract.  9  April 23, 2022  8  Improved the style and format of the content in latex.  10  May 7, 2022  8  The Lemma 2.1 was improved.  11  May 17, 2022  8  It was explicitly specified the set of natural numbers in the Lemma 2.1.  12  May 26, 2022  8   13  June 23, 2022  7  Simplified the manuscript.  14  July 2, 2022  7  We added a little detail and a single reference.  15  July 14, 2022  8  The section titled "The Main Insight" was quite difficult to understand so we explain that section further.  16  July 15, 2022  8  Last version of the author without the final revision of the referees.  17  July 16, 2022  8  Fixed theorem reference of published article of Sole and Planat. 
Keyphrases: Chebyshev function, Dedekind function, Riemann hypothesis, Riemann zeta function, prime numbers 
