R. 001, page 001, posted 2023/02/15

Replies may start by numbering. This will help for citing later. RG hasn´t implemented such. A reason may be that answers as well as replies could be erased completely. So the numbering may get confused if later counted. But nevertheless there will be an address.

Isn't it more like you're refuting the complex notation on the back of the RZF?

I'm a bit out of my league here, but going by the textbook I'd say,

1st. complex notation is a division algebra

2nd. complex functions are always mapped from C → C.

In your case of y=x2+1, if you allow x to have a complex zero, it means it is a complex number, and so you should at least plot y as a function of complex x, and then I guess you can see the zero.

The RZ "zero's" are discussed in a context of mapping the complex result ζ in the same Euclidian or Cartesian plane as the complex argument s of ζ. I found it indeed confusing, but that's how it is presented. You can also use 2 different planes.

R. 003, page 001, posted 2023/02/16

F. B.: “Isn't it more like you're refuting the complex notation on the back of the RZF?”

If a theory is to correct, it always must be corrected — what way ever it got used. If an assumption was done by the use of an inconsistent theory, it would not be true because at first (or by the way) the theory should get corrected.

F. B.: “I’m a bit out of my league here, but going by the textbook I'd say,

1st. complex notation is a division algebra”

Complex notation is on two-dimensional — except any algebra. The rules for calculating got defined separate. The two dimensions (units) are `real´ and `imaginary´. So a complex number could be seen as coordinates at the complex plane. [`a + bi´ but correct: `a, bi´]

“2nd. complex functions are always mapped from C → C.”

Euler used a complex function (his equivalence) which is on real for angle zero degree (0π by radian) or 180° degree (π by radian) and on imaginary for 90° (π/2 by radian) or 270° (3π/2 by radian). So no!

C → C is scaling as I argued at the paper.

F. B.: “In your case of y=x2+1, if you allow x to have a complex zero, it means it is a complex number, and so you should at least plot y as a function of complex x, and then I guess you can see the zero.”

Any zero of y = x2 + 1 was an assumption which got refuted at once. There are no zeros. Taking the function equal zero only then makes sense if true. Think on one-dimensional function:

y = f(x) => y = (x – x01)(x – x02) // y = x2 – 1 => y = (x + 1)(x – 1)

But on y = x2 + 1 you are not able to insert the values for the zeros. They do not exist!

The theory of complex numbers always allows the extension to complex. No proof on that. `Seeing´ the zeros of that complex function which is under examination is the point. At `z = a, bi´ a as well as b could be zero. Also a and b together could be zero. This is definition of complex number / plane. But a function of both variables (a and bi) has to depend on a single value for being a zero of a function on both. You missed the point of the proof.

F. B.: “The RZ "zero's" are discussed in a context of mapping the complex result ζ in the same Euclidian or Cartesian plane as the complex argument s of ζ. I found it indeed confusing, but that's how it is presented. You can also use 2 different planes.”

That’s the proof. Two planes are scaling; no function on two variables.

Peter,

re. my present work on the RZF I'd say I don't go as far as challenging complex notation in and of itself - but as a matter of fact I do.

Also, I don't go as far as saying, there are no zero's - but as a matter of fact I do.

Point being it seems I'm arriving at the same conclusions, which is why I noticed your remarks, albeit from a very different angle (quite literally).

Nevertheless, there is something to the effect of zero's, which can be demonstrated by creating the prime numbers.

You may agree that the "zero's" found by Riemann are the result of analytic continuation, and are not native to the RZF. Without analytic continuation there are no zero's.

My take on it is to question the use of analytic continuation, and generally, the use of the Euclidian plane / Cartesian system in number theory too prematurely.

As for your proof, which I may not entirely get:

what exactly do you mean by "scaling" - it sounds like something rather trivial?

"But a function of both variables (a and bi) has to depend on a single value for being a zero of a function on both."

Not sure if I understand this sentence. Of course for any function, to call the argument a "zero", when in fact the result is zero, is confusing, but that's the convention. In the case of a complex argument / function, a quick look up shows that it means the result is 0 + 0i, as with the RZF. That seems to me consistent. What's your point, re. "a single value"?

ps. are you planning to publish this?

R. 005, page 001

Planning to publish — yes.

Before anything clear for this, my answer comes private.

Thanks for critical reading.

Only a message for all.

Frank and me had some private posts. Frank helped to point at a bug (in meaning). So the paper will be corrected.

It was on `basing´. No, the complex function should not base on a single value, it should lead to a single value — as a special solution — for two arguments. This single value (z of f(x, y) = z) may be a zero.

Thanks, Frank!

Perhaps you could explain here why you think a complex function should have a single i.e. real result?

R. 008, page 001, posted 2023/02/20

f(x) = y = f(x) = x ... what way ever by algebraic operation at the right side, but limited on variations / extension of the single variable x .

f(x, y) = z

=> x is variable of unit X [domain1]

=> y is variable of unit Y [domain2]

and

=> z is function value of unit Z [codomain]

f(x, y) = z = algebraic operation on domain, but now on both variables.

This way z of Z is a single unit.

The third unit gets defined by algebraic operation on both the variables. This is expert opinion. [physics: z = f(x/y) = velocity = distance/time]

Note! You can´t add distance and time. They are different in unit. But velocity is defined by both on an algebraic operation.

f(x) = 10x // f(y) = 10y => coordinate (x, y) := (2, 3) [map] => (20, 30) [real]

Never to present by: f(x, y) = ...

Because that would be scaling. This example: scale 1:10 (like road-maps).

A map has no zeros.

I do not think that a complex function should have a singel result! All is on hypothetical assumtion at the proof. Taken for to help those, which couldn´t deny `complex´ at once. All on `complex´ is nonsense.

There are no zeros at `y = x2 + 1´ . The beginning failes.

Following the (inconsistant) assumtion on `complex´ leads to two independend variables (domain1 and domain2 of a complex function).

If a function of a complex construct, like f(a, bi) is, should have zeros, it can´t depent on scaling (f(a) and f(bi) seperate). So `a´ must be part of unit `REAL´, and `bi´ must be part of unit 'IMAGINARY´. `a´ is counter of measure `1´, `b´ is counter of measure `i´.

Any zero, basing on the complex plane, exclusively could depent on algebraic combination of `a´ and `b´.

Why only real (exclusively)?

This only follows the very wrong path, Riemann did. He defined separate values at the right side of the zeta-function. This is on real at one of the two units. But scaling, taken together.

So the calculation of the proof goes — limited on the real part. Out of 1/2 for real part, so out of definition of the assumtion Riemann did — what wrong way ever.

No calculation for imaginary part necessary. A nonsense-calculation for to point out that also this (nonsense) sight would be on nonsense.

All this could be seen by reading the proofs, so I thought. But no problem for the question on extended explanation.

Thanks for critical reading.

Peter,

for example this sentence, "All is on hypothetical assumtion at the proof. Taken for to help those, which couldn´t deny `complex´ at once. All on `complex´ is nonsense" I find very hard to follow grammar wise, and then we're not even talking about your proof. I think a simple Google translate of your German sentence would get you a much better result.

Either way,

- I get you physics example

- I think I get the scaling of a vector, which is just something one can do

For the rest, the RZ function is not based on "scaling", but on complex exponentiation resp. -addition. These are standard operations of this particular division algebra, creating complex results. The complex exponentiation goes like, e.g. in code:

Public Function cExp(b As Double, z As complex) As complex

If b > 0 Then a = z.im * Log(b) 'this is the angle

m = b ^ z.re 'this is the magnitude

cExp.re = m * Cos(a)

cExp.im = m * Sin(a)

cExp.arg = a

cExp.mod = m

End Function

So it's completely straightforward.

It's true that this doesn't generate zero's, meaning ζ(s) = (0 + 0i) after convergence. That is not because of the complex operations as such, but because of the complex function.

Frank,

E: All is on hypothetical assumtion at the proof.

G: Alles basiert auf hypothetischer Annahme beim Beweis.

E: Taken for to help those, which couldn´t deny `complex´ at once.

G: Genommen, um denen zu helfen, die "komplex" nicht sofort leugnen konnten.

E: All on `complex´ is nonsense.

G : Alles auf (alt.: zu) "komplex" ist Unsinn.

Google-translation is well in English/German.

The following way you argue isn´t mine. I think you had repreated expert opinion for operations done for complex expressions.

Even the way to express isn´t mine.

My work is on refuting the fundamental definitions of `imaginary´. So no work on following rules. I did that at other places. See my proof which refutes the Euler-Equivalence, for example.

Real part and imaginary part never could get added / subtracted! Euler did.

If a zero of a function of two units exists, it depents on mathematical (algebraic) combination of the two units. Riemann missed that! Using refuted definations doesn´t make an assumption being right.

Peter,

thinking critically about complex notation is good, but in the end of the day it's just a mathematical convenience one can entirely do without, both in physics and mathematics. Just look at the bit of code I copied - this is how "complex" works under the surface - simple arithmetic - and this is what really evolves the zeta function. Meaning you can also express the RZF without using complex notation - on the coding level I'm doing nothing else. What you call "opinion" is a self-consistent synthesis, which also exists for quaternions and octonions - that's the division algebra's (I think it means, if you can divide you can do all other arithmetic). Hamilton's quaternions are extremely successfully used in all 3D operations, they are the firmware of all 3D graphics cards. I've programmed quaternion rotations myself, and guess what, it all comes down to basic arithmetic and trigonometry. The moment you choose to define a complex number in the complex plane, you introduce complex vectors which behave exactly like normal vectors. Even the Euler identity can be demonstrated this way. The only "controversy" I find is the bizarre name for imaginary numbers as well as "complex numbers" - it makes completely no sense, it's just reals in an extended algebra.

Frank,

it´s not about the notation. It´s on the definition of imaginary.

[Notation `two-dimensional´ got taken by me]

You are defending the arithmetic rules which are used for complex objects. A part of my proof comes by denying `imaginary´.

So please prove it consistent that √-1 would have a basement.

√-1 => anything unknown (x) squared has to be equal -1 .

x2 = -1

Please do the simplest algebra by adding 1 at both sides:

x2 + 1 = 0

Could you see the function by this?

Please show,what way ever, how to find the zeros of that function.

Lateron, if you could do so, we may discuss your `simple arithmetic´ for `i´.

Euler used addition for the series of isin and cos . We could discuss this also later. Also the transformation for the real part `length of the vector´ for cartesian-coordinates => polar-coordinates.

Riemann has no rule for algebraic combination of real and imaginary at his equation. So no common value, which could get zero.

Peter,

You can create any complex function you like which converts to zero, and the most obvious example is a log spiral written as z=ae(k+i)θ and the arithmetic is exactly the same as for the RZF.

√-1 => anything unknown (x) squared has to be equal -1 .

x2 = -1

Please do the simplest algebra by adding 1 at both sides:

x2 + 1 = 0

x2 = -1

x = √-1

Taking x2 + 1 equal 0 is the mistake! Solve it or leave the argumentation on `imaginary´. As long as you did here, you fight without any fundamental definition which would be consistent. Doing circular arguments isn´t any proof.

Peter,

the solution is not an opinion. You could call it a "trick", but it's a "trick" that turns out to yield a broadly consistent algebra, with btw. lots of applications. This algebra is not addressed, let alone refuted, by your example - your example only shows how its unit is defined. What is a mistake, is to call the solution "imaginary". I call it a real in the complex plane. And "complex" is also not a nice term. If you have "octonions" and "quaternions", why not also have "binarions", or etc.. But other than that, one finds no controversy. It is you who is fighting an algebra in terms of another algebra without even addressing it, and what you do address, the unit "i", means nothing without its algebra. And btw. if you fight the unit "i" of complex numbers, you should also fight Hamilton's "i, j and k". I wanted to believe you're onto something that relates to my present research, but I don't see it.

Apple as a single piece — so called `element´ by expert opinion — is in singular what apples (plural) are for the set.

As long as `apple´ would be out of reality or imagination (not defined), `apples´ do not exist.

No element, no set (unit). Vice versa: no set, no element.

As long as `i´ — the element (measure) of the set `imaginary´ — doesn´t exist, the set `imaginary´ wouldn´t exist!

But it goes deeper!

The expression `-1´ as a result of a multiplication of two different quantities doesn´t exist. If no multiplication, no square-root!

Please read the proof complete.

The algebra exists. That's not the set, but then, standard algebra is not a set of reals either. As I see it you present the lack of proof of algebra_2 resp. its unit in terms of algebra_1, as a proof that algebra_2 resp. its unit does not exist. If you just say that algebra_2 resp. its unit doesn't exist in, or cannot be proven in terms of algebra_1, you may have a point, although it seems to be stating the obvious. If you nevertheless want to challenge such fundamental notions in mathematics, I'd publish it as a case in and of itself, and not use the RZF as an appetizer or trojan horse. Or to put it otherwise: it's up to you to proof that for imaginary resp. complex numbers to exist, they must be proven in real algebra.

Frank, you challenged a fundamental notion at a published paper (don´t know) and fight for its acceptance here. That is A and not A at the same time, as logic says.

Algebra is to reform, as my papers show. This goes a double way. One on old definitions, one on new. Multi-prefixed-products are very new.

I am the reformer!

It's not me who wants to change something in this field. At present I'm challenging the obviousness of analytic continuation for the RZF. Ok well then your point is not about the RZF, not even about imaginary resp. complex numbers, but about algebra itself. Btw. I just edited my previous comment. People might also like to see that your new algebra has not only the strengths of the present, but even better. "Multi prefixed products" sounds nice, I give you that :)

The reform — in use — only got taken in one part of the complete proof. The other is on missing zeros.

The reform has to be explained (very short) if used for a proof. So I did. If you want to see all about (the bridge from imaginary to real, the errors by using complex algebra ...) please look my original papers on that. No need for any horse here.

If `i´ would stay independent, why the definition on squaring? No squared apple would be a negative pear! The definition itself — by the use of algebra_1 — fails. Old math doesn´t know any multiplication (squaring if values equal) resulting negative by the use of identic prefixes of the factors.

"The definition itself — by the use of algebra_1 — fails"

That's correct, otherwise A_2 would be trivial. The fact that in A_1 "i" does not exist, makes A_2 interesting. Likewise, "j" and "k" don't exist in A_2, only in A_4, which took Hamilton a while to find out. He first tried to formulate a consistent "A_3", but it simply doesn't exist. The practical criterium is that you can do rotations by multiplication. You can do that in A_2 and A_4, and I guess in A_8.

Dodging does not solve the previous problems. You ever go deeper and deeper into the use of `imaginary´ instead of proving the basement right.

There is a clear and fundamental relation between real (:= -1) and imaginary (:= √-1). So `i´ doesn´t stay isolated. It comes constructed by an operation, well known in real-algebra, acting on a real-quantity.

Reformed math is able to solve the problem,`square-root for a result in multiplication, done by factors with different prefix´, is on.

So no bridge to reality!

Yes, √-1 shows it's a relation between two algebra's, or perhaps that A_2 incorporates A_1, it's not something in A_1 alone. So if you discuss the subject, you can't dodge the algebra, otherwise it's useless at best. Anyway I'm not the one you need to convince, but the editors / reviewers of the journal where you're going to publish your reformed math. If you want to be better prepared for that, I suggest you talk to a hard mathematician, which I'm not.

Frank, thanks for your engagement in this discussion. The core in respect to `imaginary´ got double peer reviewed. See the link given at the proof. No need to test again.

No problem. Which link is that, a published article I can check out?

Frank, see the added file.

Just as an arrival into the discussion on my part

By the kind permission of Peter Kepp and Frank van den Bovenkamp

This much I had heard about the topic of this thread :

There has gone on a lot of attempts to prove RH and the common opinion was that it is true. However ,it finally came to the notice that there were famous mathematicians: J. E. Littlewood [1], P. Turan and A.M. Turing [5, p.1209] believing that the RH is not true, e.g. the paper “On some reasons for doubting the Riemann hypothesis” (reprinted in [6, p.137]) written by A. Ivi'c

Reza Sanaye

That same paper says: "It is in the folklore that several famous mathematicians, which include P. Turan and J.E. Littlewood, believed that the RH is not true."

Frank van den Bovenkamp

So this spells that you believe it is true ??

Reza Sanaye

I don't think that what anyone believes about the RH matters much. Sure is that without the artificial intervention of analytic continuation there simply are no zero's, and I believe this is nevertheless the only way how the RZF's hidden properties can be studied. I can discuss this more when my paper is in preprint. Either way, this thread's question is not really about the RZF/ RH, but on Peter Kepp's math reform's implication for the RH.

Frank van den Bovenkamp

many thanx for the reply ........................

I now see your position ,,,,,,,,,,,

I await your coming paper ; ; ;

Meanwhile , the logics manipulation that I see Peter is doing reminds me of set zero objects which might come into play when you deactivate commutativity versus distributativity in conditions where a "group' is different from itself in that the least amount of additivity or subtractivity leads it into repetitive formations of dialogics whereby embedded bijectivities even avoid the whole standards entirely, because they are such a pain to verify. Most of the embedded morphs of logic to be imposed on the simplest levels of mathematical operations is normally in possession of pseudo-metrics that require static para-algorithmic analysis to see whether static analysis through the whole present standards defy dialogic analysis { lets name it "dialysis } if its source algorithm is even available to them the specific mathematical operation under scrutiny .

Peter Kepp

I've built an online RZF demo. It will also showcase the internal process from my upcoming paper. Best view on pc or laptop.

https://frankvandenbovenkamp.com/zetatest/

Frank van den Bovenkamp

Is it just a summary OR is that the full text ??

Reza Sanaye

It's an interactive demo. I'm not actually publishing it yet awaiting my preprint, but you could already play with the RZ standard features.

Frank van den Bovenkamp

Ok .. Alright , Sir ,,,,,,

Frank van den Bovenkamp

F. v. d. B.: “I've built an online RZF demo.”

Much work. But I only see a diagram which is two-dimensional. No imaginary part. So what is what? Riemann: f(real, imaginary) = ? [? stays for the definintion of a new unit by algebraic combination of both arguments the function is on / see on such complete real]

If a function is on two dimensions (so complex is / real, imaginary), the zeros of any function of a complex argument must be on a third dimension (unit).

Please read the given start for this discussion again very carefully.

Peter Kepp

Thanks for checking it out.

The zeta function combines the Re and Im of the argument, the demo does the prescribed arithmetic.

I equally agree that there are no zero's, but that's because I don't use analytic continuation (AC).

As for the demo, what you see is the standard Im part of the function plotted against the Re part. Of course there's various other ways as well.

I do argue though that the conflation of number theory and complex analysis is not as straightforward as it seems, which obviously has a bearing on the RZH and perhaps on your point as well.

Frank: “The zeta function combines the Re and Im of the argument, the demo does the prescribed arithmetic.”

•••

No! It doesn´t. Riemann presents left side: f(complex) and also right side: complex as isolated units! No combination.

f(x, y) = a(x, y) is scaling, no combination. f(x, y) = 3x + 4y2 is combination!

Please show the rule of combinig real and imaginary.

If I would use any hocus pocus, all could happen at math. I argued twice. At old fashioned way and by reformed math.

•••

You gave the proof:

Frank: “As for the demo, what you see is the standard Im part of the function plotted against the Re part. Of course there's various other ways as well.”

•••

That´s on two dimensions, no functional common value, to depict at a third axis, so scaling!!!

Complex analysis bases on number-theory — as the best.

Peter Kepp

"Scaling" means that everything gets proportionally bigger. The RZF doesn't do that. That is, in fact the real part does that more or less, whereas the im part imparts a rotation. The rule that combines the two is the zeta function, using basic complex arithmetic. The combined result is what you see. In short I can't see how any f(x, y) = a(x, y) amounts to scaling, unless for special f's perhaps. If the RZF just did scaling, it was a nothing burger.

btw it's f(xarg, iyarg) = (xresult, iyresult). If you say that it's strange to assume them in the same plane, I agree. It's basically incorrect. But that's just the routine, because paper happens to be 2D. Ideally it would be 3+1D, i.e. 3D + e.g. a color code. But that's done as well!

Frank van den Bovenkamp

F. B.:“ “Scaling" means that everything gets proportionally bigger.”

That is a too much restricted definition of `scaling´, as I meant it. Think on lensing ... . `f´(...) is not specified, all is possible.

F. B.:“f(xarg, iyarg) = (xresult, iyresult)”

This is half the right way! `The same plane´ could be done at a plane paper using another part of its area. But again you give the proof. Arguments are of different unit, results are of different unit.

f(x) = y better is to present by complete quantities: f(a[1] x) = f(a)[1] y

This is two dimensional, one dimension for argument, one for result. The mathematical composition is restricted on the number (of amount) of the argument. No handling on the measure of the argument! But you (as well as Riemann) did.

f(a[1] real, b[i] imaginary) = (a combined with b)[new measure] new unit

The highlighted (bold) only could be the function. Riemann fails!

The confusing results, you calculated, bases on the misleading theory for handling complex. This is special part of the proof.

Your calculation is depicting at a plane (scaling). A plane has no hight. The hight of a plane could be positive or negative. The third value comes by the zeros.

RZF has no zeros!

Peter Kepp

"Arguments are of different unit, results are of different unit."

Yes, but only to the extend that in a real function y=f(x), x, and y are of different unit.

Other than that I don't see why complex functions are different than real functions with two real arguments. Again, I've done and programmed the function, and it's all done with standard arithmetic and trigonometry. The unit "i" has no role in it - it's in fact merely a sort of emerging invariance in said arithmetic, which one may or may not consider, but the existence of which cannot be denied. In the end "i" is just a quite remarkable convenience for many uses.

Here's the code for complex exponentiation:

Public Function cExp(base As Double, z As complex) As complex

If base > 0 Then angle = z.im * Log(base)

magnitude = base ^ z.re

cExp.re = magnitude * Cos(angle)

cExp.im = magnitude * Sin(angle)

cExp.arg = angle

cExp.mod = magnitude

End Function

The imaginary compartmentalization does not remain of the same dimension all throughout the processualization of complex functions . Even self-determination is ensconced in a sphere where the focus is not on mathematical rigor but rather on collecting some bits of data on the functionals [ of the originary function ] on the very powerful machinery of manifolds and “post-Newtonian calculus”. The systematics of functional differential equations does not have a continuously differentiable solution for every value of the parameter , say , a .

Reza Sanaye

I think I understand what you're saying - the meaning of "i" is not the same in all of topology. To me that signals that complex operation is useful at many places, but may be superseded by topology.

Frank van den Bovenkamp

my take is that you are expressing the idea even better than me !!

I precisely meant that ...........

Appreciations , Mr Bovenkamp !!

Reza Sanaye

Well, that's sure something to think of. It raises the question what the use of complex notation implicates wrt. to topological stability. If it (unwittingly) introduces more degrees of freedom / independent dimensions than warranted, this would raise an alert. Iow. I'm wondering to what extend the routine of complex notation contributed to the 4D paradigm we're stuck with.

Now , Dear Frank van den Bovenkamp !

I ask for the permission to talk with some level of authority on this specific issue which you appear to have grasped very well . First of all, Thank you for understanding the depth of it so acutely . Second of all , I let myself speak about this a tiny bit authoritatively for the very plain reason that I have been spending quite much time on that . A complex spacetime geometry refers to the metric tensor being complex, not spacetime itself. Also , Everything that we measure the velocity to acceleration for an object has to have a frame of reference which is nothing but a physical reference point. An inertial reference frame is either at rest or moves with a constant velocity. Non−inertial reference frame is a reference frame that is accelerating either in linear manner or rotating around some axis. The Minkowski space of special relativity (SR) and general relativity (GR) is a 4 dimensional " pseudo-Euclidean space " vector space. The Einsteinian one isn't . That’s because of the facticity that they really are extremely complicated, but it might not be obvious if you’re using the very compact tensor notation.

The late Prof. Einstein made it nearly completely obfuscated . In reality, HIS equation really includes 16 different equations, one for each combination of µ and ν, which can both be either 0,1,2 or 3 (in reality, there is actually only 10 independent equations due to some symmetry properties). That also tries to ignore dissipative vibratory intrinsics of the GRUND ,too. Added to the intentional complexity is that these quantities [ Einstein field ones ] seen in the usual form of the field equation are actually even yet much more complicated. I do not see why they have necessarily been written so complicated . I cannot see . They ought to have been far way simpler as fundamentally they all contain the metric tensor gµν.

Frank, as I said, you use mathematical rules which got refuted.

Whatever you have calculated the result is on two seperate units. No common value less than zero, zero, more than zero.

Please Reza and Frank, concentrate on the topic. Only `imaginary´ math, no relativistic theories here!

Frank, your routines got refuted by me! Doing the wrong again doesn´t make it right! And you said it more times: if there are no zeros (your opinion too) all is `nothing burger´. I am (a real) Ham-burger. So of living meat. Beware of the snappy Hamburger!

The topic could be out. No refutation. But the problem with RG, in difference to the `Nobel-World´, is on being inverse. The one who gets the Nobel-award does the `proof´ and is of interest for all of his topic.

Not so at RG.

If one does his proof at RG, nearly all are still.

Does this depent on the selection one will come to RG?

Peter:

as as result of your reaction on the other thread I leave this discussion.

What a discussion do you mean? You ever argue beneth the topic! You try to confuse the silent readers. No help, even at the deepest level, is fruitful for you. As I said, the topic is out without any contra.

Thanks anyway. It helps extending the argumentation.

Peter, I agree that [most] current thinking & analysis are inadequate & misguided (wrong-headed, i.e. hopeless). However, understanding the core issue of RH requires accepting the real issue:

Why are any zeta zeros where they are when "s" = 1/2?

As you must know, many trillions of "nontrivial" zeros have been verified, but most mathematicians keep failing to see the "trivial" zeros as equally significant.

And where is your reply? Did you read the initiating article?