Investigation of Riemann hypothesis via Rényi dimension and Hurst exponent

• Main Author: Peh, Wei Yan
• Other Authors: Shu Jian Jun
• Format: Final Year Project
• Language: English
• Published: 2018
• Subjects: DRNTU::Engineering::Mathematics and analysis::Simulations; DRNTU::Engineering::Computer science and engineering::Mathematics of computing::Numerical analysis; DRNTU::Engineering::Computer science and engineering::Mathematics of computing::Probability and statistics; DRNTU::Science::Mathematics::Applied mathematics::Signal processing; DRNTU::Science::Mathematics::Statistics; DRNTU::Science::Mathematics::Number theory; DRNTU::Science::Mathematics::Applied mathematics::Data visualization
• Online Access: http://hdl.handle.net/10356/74656
• Institution: Nanyang Technological University

The Riemann hypothesis is an unsolved problem in mathematics involving the locations of the non-trivial zeros in the Riemann zeta function, and state that: "The real part of every non-trivial zero of the Riemann zeta function is 1/2." This means all non-trivial zeros must lie along a critical line composes of complex numbers with Re(s) = 1/2 . The final year project assesses the possible application of the Rényi dimension and Hurst exponent to study the Riemann zeta function and the Riemann hypothesis. The results obtained from the algorithms when applied to the Riemann zeta function along the critical line shows that the zeta function became more fractured and anti-persistent along the critical line. This implies that these two methods are able to yield correct results and thus is a feasible way to tackle the Riemann hypothesis.