Download PDFOpen PDF in browserCurrent versionThe Riemann HypothesisEasyChair Preprint no. 3708, version 45Versions: 12345678910111213141516171819202122232425262728293031323334353637383940414243444546474849505152→history 14 pages•Date: March 30, 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 $\frac{1}{2}$. In 2002, Lagarias proved that if the inequality $\sigma(n) \leq H_{n} + exp(H_{n}) \times \log H_{n}$ holds for all $n \geq 1$, then the Riemann Hypothesis is true, where $\sigma(n)$ is the sumofdivisors function and $H_{n}$ is the $n^{th}$ harmonic number. We prove this inequality holds for all $n \geq 1$ and therefore, the Riemann Hypothesis must be true. Keyphrases: Divisor, inequality, number theory
