Reitsma, Theunis (2020) Numerically testing the Riemann hypothesis. Bachelor's Thesis, Mathematics.
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Abstract
The Riemann Hypothesis states that all non-trivial zeros of the Riemann zeta function lie on the complex line 1/2+it for a real number t. In this bachelor’s thesis we study a way to prove this hypothesis for |Im(z)|=r, with r real and z complex. The zeta function is a complex function given by an infinite sum in a part of the complex plane and analytic continued to the whole complex plane. It will be proven that the zeros of this function are all inside the complex strip with 0<Re(z)<1. After that, a contour integral will be computed numerically around this strip up to |Im(z)|<r, to prove the Hypothesis. The zeta function is a special case of so-called L-functions. The method as described above will also be applied to an L-function of an elliptic curve to prove that its zeros are at the critical line of this L-function.
| Item Type: | Thesis (Bachelor's Thesis) |
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| Supervisor name: | Top, J. and Djukanovic, M. |
| Degree programme: | Mathematics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 14 Jul 2020 10:34 |
| Last Modified: | 14 Jul 2020 10:34 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/22680 |
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