Download PDFOpen PDF in browserCurrent versionThe Riemann HypothesisEasyChair Preprint no. 3708, version 47Versions: 12345678910111213141516171819202122232425262728293031323334353637383940414243444546474849505152→history 4 pages•Date: May 7, 2021AbstractLet's define $\delta(n) = (\sum_{{q\leq n}}{\frac{1}{q}}\log \log nB)$, where $B \approx 0.2614972128$ is the MeisselMertens 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
