find zeros of the Riemann zeta function

Version 1.0.2 (9,01 ko) par Thomas
This function finds zeros of the Riemann zeta function on the critical line 0.5 + i*t in an interval von <= t <= bis
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Mise à jour 25 déc. 2021

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Run [Zeros = findZerosRiemannZetaSiegel2(von, bis, steplength) to find zeros of the Riemann zeta function on the critical line 0.5 + i*t in the intervail von <= t <= bis
The function mainly looks for sign changes in the real and imaginary part. The values are calculated using the Riemann-Siegel formula.
There is no gurantee to find all zeros, since some sign changes occur within very short distances and can be skipped. E.g: the real part of the zero for t=122.946829294... is below zero only for a tiny interval of t. So choose steplength sufficiently small!
Example: findZerosRiemannZetaSiegel(120, 130,0.01) will produce:
121.3701 121.3700 121.3800
124.2568 124.2500 124.2600
127.5167 127.5100 127.5200
129.5787 129.5700 129.5800
.... not finding the zero at t=122.946829294....
Try to run: findZerosRiemannZetaSiegel(120, 130,0.002) and the function will find it.

Citation pour cette source

Thomas (2024). find zeros of the Riemann zeta function (https://www.mathworks.com/matlabcentral/fileexchange/84265-find-zeros-of-the-riemann-zeta-function), MATLAB Central File Exchange. Extrait(e) le .

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Version Publié le Notes de version
1.0.2

Better performance. Also uses parallel toolbox now.

1.0.1

added output graph (commented out, but comment back in, if needed).

1.0.0