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      One-Click Submission System Now Available for SO Preprints, learn more on how this works in our blog post and don't forget to check the video, too!

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      Version and Review History
      Preprint version 2
      Preprint version 1
       
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      Author(s):   1 ,
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      Journal: ScienceOpen Preprints
      Publisher: ScienceOpen
      Keywords: Riemann hypothesis, Cramér's conjecture, prime numbers, Riemann zeta function, Chebyshev function
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            Abstract

            Content

            Author and article information

            Journal
            Title: ScienceOpen Preprints
            Publisher: ScienceOpen
            Publication date (Electronic preprint): 6 March 2024
            Affiliations
            [1 ] GROUPS PLUS TOURS INC., 9611 Fontainebleau Blvd, Miami, FL, 33172, USA;
            Author notes
            Author information
            https://orcid.org/0000-0001-8210-4126
            Article
            DOI: 10.14293/PR2199.000744.v1
            SO-VID: 4e40e35d-073b-460b-b77c-67c65021cedb
            License:

            This work has been published open access under Creative Commons Attribution License CC BY 4.0 , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Conditions, terms of use and publishing policy can be found at www.scienceopen.com .

            History
            Date received : 6 March 2024
            Categories

            Data availability: Data sharing not applicable to this article as no datasets were generated or analysed during the current study.
            ScienceOpen disciplines: Number theory
            Keywords: Riemann hypothesis,Cramér's conjecture,prime numbers,Riemann zeta function,Chebyshev function

            References

            1. Connes Alain. An Essay on the Riemann HypothesisOpen Problems in Mathematics. p. 225–257. 2016. Springer International Publishing. [Cross Ref]

            2. Euler's Totient FunctionEquivalents of the Riemann Hypothesis. p. 94–143. Cambridge University Press. [Cross Ref]

            3. Ayoub Raymond. Euler and the Zeta Function. The American Mathematical Monthly. Vol. 81(10)1974. JSTOR. [Cross Ref]

            4. Nicolas Jean-Louis. Petites valeurs de la fonction d'Euler. Journal of Number Theory. Vol. 17(3):375–388. 1983. Elsevier BV. [Cross Ref]

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