Javascript must be enabled for the correct page display

Numerically testing the Riemann hypothesis

Reitsma, Theunis (2020) Numerically testing the Riemann hypothesis. Bachelor's Thesis, Mathematics.

[img]
Preview
Text
bMATH_2020_ReitsmaT.pdf

Download (592kB) | Preview
[img] Text
toestemming.pdf
Restricted to Registered users only

Download (95kB)

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)
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

Actions (login required)

View Item View Item