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The Riemann Hypothesis

EasyChair Preprint no. 3708, version 47

4 pagesDate: May 7, 2021


Let's define $\delta(n) = (\sum_{{q\leq n}}{\frac{1}{q}}-\log \log n-B)$, where $B \approx 0.2614972128$ is the Meissel-Mertens constant. The Robin theorem states that $\delta(n)$ changes sign infinitely often. We prove if the inequality $\delta(p) \leq 0$ holds for a prime $p$ big enough, then the Riemann Hypothesis should be false. However, we could restate the Mertens second theorem as $\lim_{{n\to \infty }} \delta(p_{n}) = 0$ where $p_{n}$ is the $n^{th}$ prime number. In this way, this work could mean a new step forward in the direction for finally solving the Riemann Hypothesis.

Keyphrases: Divisor, inequality, number theory

BibTeX entry
BibTeX does not have the right entry for preprints. This is a hack for producing the correct reference:
  author = {Frank Vega},
  title = {The Riemann Hypothesis},
  howpublished = {EasyChair Preprint no. 3708},

  year = {EasyChair, 2021}}
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