Download PDFOpen PDF in browserCurrent versionThe Riemann Hypothesis Is Possibly TrueEasyChair Preprint no. 7094, version 16 pages•Date: November 27, 2021AbstractIn mathematics, the Riemann hypothesis is a conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part $\frac{1}{2}$. The Riemann hypothesis belongs to the David Hilbert's list of 23 unsolved problems and it is one of the Clay Mathematics Institute's Millennium Prize Problems. The Robin criterion states that the Riemann hypothesis is true if and only if the inequality $\sigma(n)< e^{\gamma } \times n \times \log \log n$ holds for all natural numbers $n> 5040$, where $\sigma(x)$ is the sumofdivisors function and $\gamma \approx 0.57721$ is the EulerMascheroni constant. The Nicolas criterion states that the Riemann hypothesis is true if and only if the inequality $\prod_{q \leq q_{n}} \frac{q}{q1} > e^{\gamma} \times \log\theta(q_{n})$ is satisfied for all primes $q_{n}> 2$, where $\theta(x)$ is the Chebyshev function. Using both inequalities, we show that the Riemann hypothesis is possibly true. Keyphrases: Chebyshev function, Nicolas inequality, prime numbers, Riemann hypothesis, Riemann zeta function, Robin inequality, sumofdivisors function
