The Riemann Hypothesis: A Fresh and Experimental Exploration
Sergio Da Silva
*
Department of Economics, Federal University of Santa Catarina, 88049-970, Florianopolis, Brazil.
*Author to whom correspondence should be addressed.
Abstract
This research proposes a new approach to the Riemann Hypothesis, focusing on the interplay between prime gaps and the non-trivial zeros of the Riemann Zeta function. Utilizing various statistical models and experimental analysis techniques, three important insights are uncovered: 1) Granger causality tests reveal a predictive relationship in which past non-trivial zeros may predict future prime gaps; 2) Complex, nonlinear interactions between prime gaps and non-trivial zeros are identified, challenging simple linear correlations; and 3) Causal network analysis reveals intricate feedback-loop relationships. These findings contribute to a better understanding of prime number distribution and the Zeta function, opening up novel possibilities for further mathematical research. The study aims to motivate mathematicians towards a proof or disproof of the Riemann Hypothesis.
Keywords: Riemann hypothesis, prime gaps, non-trivial zeros of the zeta function, statistical models