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A Very Brief Note on the Riemann Hypothesis

EasyChair Preprint no. 8557, version 8

7 pagesDate: August 16, 2022

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.

Keyphrases: prime numbers, Riemann hypothesis, Robin's inequality, sum-of-divisors function, Superabundant numbers

BibTeX entry
BibTeX does not have the right entry for preprints. This is a hack for producing the correct reference:
@Booklet{EasyChair:8557,
  author = {Frank Vega},
  title = {A Very Brief Note on the Riemann Hypothesis},
  howpublished = {EasyChair Preprint no. 8557},

  year = {EasyChair, 2022}}
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