What do you think of Dimitrii Kouznetsov's article?

[Shanghai46]

I've been browsing on the internet about tetration, and I've found an article which is very promising about tetration. It's a bit to complex for me to understand, but I'm just wondering if this work is credible and rigorous. So tell me what you think about this article!
https://en.citizendium.org/wiki/tetration

[Daniel]

I've been browsing on the internet about tetration, and I've found an article which is very promising about tetration. It's a bit to complex for me to understand, but I'm just wondering if this work is credible and rigorous. So tell me what you think about this article!
https://en.citizendium.org/wiki/tetration

I'll drop a quick answer until someone else more knowledgeable comes along. Kouznetsov's work and his work with Bo are very important. Their papers around 2007 may have been the first published papers on extending tetration. Like everyone else until Paulsen, they were unable to find a way to master the convergence of tetration. Paulsen mentions that his work is consistent with Kouznetsov's (maybe based on Kouznetsov's?)  I consider it an serious intellectual failing that I have not mastered their material. So the material is both credible and rigorous, and dare I say required reading here.
On a personal note, I understand Kouznetsov is living in Moscow now. I hope he is doing well.

Also, see https://math.eretrandre.org/tetrationfor...y#pid10312

[JmsNxn]

I've been browsing on the internet about tetration, and I've found an article which is very promising about tetration. It's a bit to complex for me to understand, but I'm just wondering if this work is credible and rigorous. So tell me what you think about this article!
https://en.citizendium.org/wiki/tetration

I'll drop a quick answer until someone else more knowledgeable comes along. Kouznetsov's work and his work with Bo are very important. Their papers around 2007 may have been the first published papers on extending tetration. Like everyone else until Paulsen, they were unable to find a way to master the convergence of tetration. Paulsen mentions that his work is consistent with Kouznetsov's (maybe based on Kouznetsov's?)  I consider it an serious intellectual failing that I have not mastered their material. So the material is both credible and rigorous, and dare I say required reading here.
On a personal note, I understand Kouznetsov is living in Moscow now. I hope he is doing well.

Also, see https://math.eretrandre.org/tetrationfor...y#pid10312

Kouznetsov is a great genius. My only criticism, is that he uses too much heuristic reasoning. Paulsen's paper, takes a lot of credit from Kouznetsov; but it is largely a reconstruction of Kneser's work. What Paulsen takes from Kouznetsov, primarily, is the "Race Track Method". This is an integral transform method to calculate tetration (to be a calculator, stuff). Paulsen presents Kneser's method, but then uses much of the numerical methods Kouznetsov worked out. But still, Kouznetsov wrote much more detailed analysis than Paulsen. Paulsen was just more rigid, refined and rigorous--focused on one problem. But they took a lot from Kouznetsov's work; and Trapmann.

Kouznetsov is also a bit of a polyglot. I talked to him in french and english; while he talked to Trapmann in german--all while his language of choice is russian. I do think, some of his math is too much "well the numbers work so let's move on". Where he doesn't "prove" these things in a rigorous mathematical setting. He's still right in any experimental sense.

To me; Kouznetsov's work represents very accurate descriptions of Kneser, and the like. But it isn't hard core "epsilon delta" proven. So yes, the numbers work out, as they should. But his proofs are lacking. Despite being entirely correct.

Dude's smart as fuck though. And OP, I highly suggest reading his textbook. He's definitely "more physicist" than "mathematician" if that makes sense.   Fitting when he works for laser companies in russia, lmao.

---

And towards, OP:

But, if I can answer your question. The link you gave is a very good source; but it's not a perfect source. The conclusion of the math will be the same; but if you were to press Kouznetsov to give \(\epsilon/\delta\) proofs he will fail. This is a big problem here, to actually mathematically prove that this approach works. The numbers work, and produce feasible numbers. But we can't \(\epsilon/\delta\)-prove it.

So yes, the source you are showing is a great source. Just remember, it's not rigorously proven. Just because it looks like it converges nice, doesn't mean it does. But we all are pretty sure it does converge as nice as he says

Ya, all the graphs of the riemann zeta functions show the zeroes are at \(b= 1/2 + it_0\)--proving it is another thing, lol.