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https://hdl.handle.net/10356/74656
Title: | Investigation of Riemann hypothesis via Rényi dimension and Hurst exponent | Authors: | Peh, Wei Yan | Keywords: | 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 |
Issue Date: | 2018 | Abstract: | 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. | URI: | http://hdl.handle.net/10356/74656 | Schools: | School of Mechanical and Aerospace Engineering | Rights: | Nanyang Technological University | Fulltext Permission: | restricted | Fulltext Availability: | With Fulltext |
Appears in Collections: | MAE Student Reports (FYP/IA/PA/PI) |
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File | Description | Size | Format | |
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FYP Report.pdf Restricted Access | Final Year Project Report | 4.47 MB | Adobe PDF | View/Open |
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