A Short Disproof of the Riemann Hypothesis - Armando M. Evangelista Jr. (Zenodo, 2018)
The Riemann Hypothesis is one of the most important unsolved problem in Mathematics: its validity will have have a great consequence on the precise calculation of the number of primes. Riemann developed an explicit formula relating the number of primes with the hypothesized non-trivial zeros of the Riemann zeta function. Riemann hypothesis states that all the non-trivial zeros of the zeta function have real part equal to one-half on the critical strip.
Despite many attempts to solve it for about 150 years, no one have, so far succeeded. Riemann hypothesis is based on the existence of the zeros of the zeta function. If it can be shown, that, such zeros do not exist, then, the Riemann Hypothesis is false.