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[Corrigendum] Note on the Riemann Hypothesis: International Conference on Recent Developments in Mathematics (ICRDM 2022)

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  • Author(s): Vega, Frank
  • Document Type:
    other/unknown material
  • Language:
    unknown
  • Additional Information
    • Publication Information:
      Cambridge University Press (CUP)
    • Publication Date:
      2023
    • Abstract:
      Robin's criterion states that the Riemann hypothesis is true if and only if the inequality $\sigma(n) < e^{\gamma} \cdot n \cdot \log \log n$ holds for all natural numbers $n > 5040$, where $\sigma(n)$ is the sum-of-divisors function of $n$ and $\gamma \approx 0.57721$ is the Euler-Mascheroni constant. We require the properties of superabundant numbers, that is to say left to right maxima of $n \mapsto \frac{\sigma(n)}{n}$. In this note, using Robin's inequality on superabundant numbers, we prove that the Riemann hypothesis is true. This is a "Corrigendum" for a paper presentation at the ICRDM 2022 held at Canadian University Dubai, Dubai, UAE during 24-26 August 2022. Besides, this proof is an extension of the article "Robin's criterion on divisibility" published by The Ramanujan Journal on May 3rd, 2022.
    • Accession Number:
      10.33774/coe-2023-tbh0z
    • Online Access:
      https://doi.org/10.33774/coe-2023-tbh0z
      http://dx.doi.org/10.33774/coe-2023-tbh0z
      https://www.cambridge.org/engage/api-gateway/coe/assets/orp/resource/item/6485048fbe16ad5c57bff76a/original/corrigendum-note-on-the-riemann-hypothesis-international-conference-on-recent-developments-in-mathematics-icrdm-2022.pdf
    • Rights:
      https://creativecommons.org/licenses/by/4.0/
    • Accession Number:
      edsbas.CA0967CF