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This is an Argand diagram showing the first 40,000 terms of the series form of the Riemann Zeta function, for the argument ##\sigma + i t = 1/2 + 62854.13 \thinspace i##

The blue lines are the first 100 (or so) terms, and the rest of the terms are in red. The plot shows a kind of approximate symmetry about the dotted green line, in the sense that the red part mirrors the blue part on average but is much more fine-grained. The last spiral in the red part is centred around the analytically continued value of zeta.

These aspects of the RZF seem rather interesting to me, but I could find only a limited amount of discussion about it --

1. https://arxiv.org/abs/1310.6396, G. Nickel, Geometry of the Riemann Zeta Function

2. https://arxiv.org/abs/1507.07631, G. Nickel. Symmetry in Partial Sums of the Riemann Zeta Function

3. https://ojs.stanford.edu/ojs/index.php/surj/issue/download/surj-2005/47, see pages 17-26.

4. http://laacademy.org/LAS2021/posters/P24_Conor_McGibboney.pdf

I am wondering why there isn't more interest in this. Is it because it is considered a dead end as far as research level mathematics?

Secondly, are there other sources that I have missed?

Thirdly, the symmetry property is not actually proved in the above references, but only explored phenomenologically. Is there a rigorous proof somewhere?

The blue lines are the first 100 (or so) terms, and the rest of the terms are in red. The plot shows a kind of approximate symmetry about the dotted green line, in the sense that the red part mirrors the blue part on average but is much more fine-grained. The last spiral in the red part is centred around the analytically continued value of zeta.

These aspects of the RZF seem rather interesting to me, but I could find only a limited amount of discussion about it --

1. https://arxiv.org/abs/1310.6396, G. Nickel, Geometry of the Riemann Zeta Function

2. https://arxiv.org/abs/1507.07631, G. Nickel. Symmetry in Partial Sums of the Riemann Zeta Function

3. https://ojs.stanford.edu/ojs/index.php/surj/issue/download/surj-2005/47, see pages 17-26.

4. http://laacademy.org/LAS2021/posters/P24_Conor_McGibboney.pdf

I am wondering why there isn't more interest in this. Is it because it is considered a dead end as far as research level mathematics?

Secondly, are there other sources that I have missed?

Thirdly, the symmetry property is not actually proved in the above references, but only explored phenomenologically. Is there a rigorous proof somewhere?

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