Isn't the Riemann Hypothesis just a convention?

[mustang19]

If the zeta function intersects the critical line when the real part is 1/2, then it will intersect some other line when some other real part is used. Isn't the Riemann Hypothesis just based on a particular convention for the critical line?

 

[stevendaryl]

I don't understand your question. The Riemann hypothesis is that if $\zeta(s) = 0$, then either $s$ is a negative integer, or its real part is 1/2. I don't see how that can be a matter of convention.

 

[mustang19]

I don't understand your question. The Riemann hypothesis is that if $\zeta(s) = 0$, then either $s$ is a negative integer, or its real part is 1/2. I don't see how that can be a matter of convention.

Well why are we concerned with z(s) = 0? We could base our prime counting on any pattern found in any z(s).

 

[mfb]

We could base our prime counting on any pattern found in any z(s).

What do you mean by that?

ζ(s)=0 is special. For every non-zero value, we know it is attained elsewhere. Only for zero it is still unclear. There is no uncertainty about ζ(s)=1, or ζ(s)=i, or similar values, for example.The Riemann hypothesis has applications beyond the prime numbers.

 

[mustang19]

What do you mean by that?

ζ(s)=0 is special. .

So it sounds like RH is just the "everything else" of mathematics. Any roots which aren't otherwise explained fall under RH. Sounds absolutely impossible to solve.

 

[mfb]

I don't understand your last post. And now I don't think I understand your other posts either.

 

[Ssnow]

If the zeta function intersects the critical line when the real part is 1/2, then it will intersect some other line when some other real part is used.

I don't understand the question but the problem for the zeta function is exactly that it seems to have zeros when the real part of $z$ is $\frac{1}{2}$ other lines are not so interesting ...

 

[mustang19]

Well I guess primes will always be odd and if you divide them in half you will get an even number plus 1/2. Brb going to publish

 

[mfb]

Your post has absolutely no connection to the zeta-function or the Riemann hypothesis.

 

[mustang19]

Well how about this. Let f(x) be whatever function makes the equation work. The denominator is the zeta function can be rewritten as (n^1/2)(n^f(x)). Because taking a square root requires you to factor out the perfect squares in the radicand, you will end up with

Sqrt(perfect squares)*(n^f(x))

So the 1/2 just provides the list of perfect squares to be excluded from the result by the rest of the function.

 

[stevendaryl]

Well how about this. Let f(x) be whatever function makes the equation work.

What equation?

The denominator is the zeta function can be rewritten as (n^1/2)(n^f(x)). Because taking a square root requires you to factor out the perfect squares in the radicand, you will end up with

Sqrt(perfect squares)*(n^f(x))

So the 1/2 just provides the list of perfect squares to be excluded from the result by the rest of the function.

It's difficult to know what in the world you are talking about. What equation are you talking about? What denominator are you talking about? Why are you talking about taking a square-root?

We have a well-defined function, $\zeta(s)$, which for real $s > 0$ can be written as $\sum_n n^{-s}$, but which can be analytically extended to complex values of $s$. When we try to look for values of $s$ making $\zeta(s) = 0$, we find find solutions for:

$s = -2, -4, -6, ...$

and for values of the form

$s = +1/2 + i x$

The conjecture is: All zeros of $\zeta(s)$ are of this form. It's just one of those conjectures, like Fermat's last theorem, that seems to be true, but nobody has a proof. It's definitely not "just a convention", so that's the answer to your original question, isn't it? Have you changed to a different question, or are you still wondering whether it's just a convention?

 

[mustang19]

I am just saying that there are relations between perfect squares and primes that you can exploit to locate primes, this is what the zeta function does and the 1/2 power provides a means to locate perfect squares.

 

[mfb]

That doesn't make sense. Multiple members in multiple threads told you that you are wrong with your interpretation of the zeta function. How many more threads do you plan to make?

 

[mustang19]

Well I am sure you know that you can count primes using the interval between two perfect squares, if this is not what the zeta function does to find primes then Id be interested in knowing what it actually does.

 

[RockyMarciano]

If the zeta function intersects the critical line when the real part is 1/2, then it will intersect some other line when some other real part is used. Isn't the Riemann Hypothesis just based on a particular convention for the critical line?

If you mean that the RH is unprovably true(so it is either an independent new or known axiom in disguise) this has been suspected by many mathematicians from the moment the hypothesis was formulated, but then again a solid proof of undecidability in the vein of Godel's theorems is needed. It's not the kind of question that can be answered: "Oh yeah, that's right, it's just a convention. Next question?"

 

[Demystifier]

Why do math crackpots always work on number theory?

 

[mustang19]

You could write any variation of the zeta function for any critical line. Whatever critical line you pick is completely arbitrary. That is why asking about it is useless, because it is already predetermined by the assumptions you made when creating the function.

 

[jedishrfu]

3brown1blue has a great video explaining the Riemann Zeta function on youtube:

 

[mustang19]

That's a great video. Anyway these guys are 2 days from solving the riemann hypothesis, they just made a simple physical model.

https://www.google.com/amp/s/phys.org/news/2017-04-insight-math-million-dollar-problem-riemann.amp

 

[jedishrfu]

Why do math crackpots always work on number theory?

Because they don't know enough physics.

 

[RockyMarciano]

That's a great video. Anyway these guys are 2 days from solving the riemann hypothesis, they just made a simple physical model.

https://www.google.com/amp/s/phys.org/news/2017-04-insight-math-million-dollar-problem-riemann.amp

Unfortunately here( https://arxiv.org/abs/1704.02644 ) is shown that line of attack doesn't hold water.

 

[mustang19]

It was published in prl. I assume they would have caught that in peer review if the flaw was that trivial.

 

[jedishrfu]

Unfortunately here( https://arxiv.org/abs/1704.02644 ) is shown that line of attack doesn't hold water.

The arxiv paper is a comment on the Physics Review article and I don't think the comment has been peer reviewed.

 

[Demystifier]

Because they don't know enough physics.

Enough for what? For being a physics crackpot?

 

[jedishrfu]

Enough for what? For being a physics crackpot?

Yep.

 

[mustang19]

If the zeta function intersects the critical line when the real part is 1/2, then it will intersect some other line when some other real part is used. Isn't the Riemann Hypothesis just based on a particular convention for the critical line?

Oh and the distances between two numbers are always powers of 1/2 anyway.