Riemann zeta function

[XxCHRISTIANxX2001]

whats the point of this?

[funChick84]

This is really amazing stuff, i hope to learn this material some day looks very challenging and exotic. Funny how i landed here i was reading about Gauss and scrolled down to find riemann now i cant stop watching all these videos. Ya i may not understand it but like i said someday maybe hopefully :)

[meatisdeliciouse]

The zeta function is amasing, I have tried to talk to my maths techeacher, excusse my spelling. Doesnt it also fit into DNA too? Maths is amasing, the only way we can comunicate with extra terestrials really.

[meatisdeliciouse]

This is so incredibly complicated, I cant even explain it to anyone. Didnt the find out that prime number directly corolate to the way atoms are built, if you translate them through the zeta function? I herd somewhere that the zeta function can even help to build the perfect amphithetre, I may be very inteligent, but how on earth do people actualy descover this, I mean it's so incredibly complicated, even I don't understand it all!!

[monobrowperson]

I found a zero that is not on the line. However, I also discovered an application to HAARP. Therefore, I won't disclose my secret. The Japanese will understand why.

[phicomingatya]

@monobrowperson lol, very funny!

[Frisbieinstein]

The function is purposefully constructed so that the zeros are the primes. That's not the mystery. Why are they all on the 1/2 strip? There seems to be no reason at all for that.

[phicomingatya]

@Frisbieinstein There is reason for all zeros to be on 1/2 strip. It's because the prime zeta function has a singularity at s=1/2, which makes it possible for the zeta to have zeros on the line Re(s)=1/2.

[gae3tano]

excuse me, but i don't undestand what are the real relations between the zero's on the critical line of rienmann hypotesys and prime numbers..there's somebody who can to explain that relations!??thancks

[sitwosaints]

Fonsidream, I don't think your grave concerns need concern us. I think you write ( as we say in England ) in green ink.

[ryoryo8888]

You reminded me the beauty of mathematics!

Thank you.

[MrHacker3000]

that look like Mathematica!! :D

[theCamelCase]

Nothing beats visualization for guiding understanding. Well done.

[NvidiaPWND]

this is great man!

[black6moon]

Hermoso simplemente hermoso pero tenia entendido que la funcion z es valida solo en una parte del plano y que despues para el valor de -1 es=-1/12 algo asi

[ortega24024]

Eso está correcto. Valor de zeta(-n) es (-1)^n B_ {n+1}/(n+1), donde está un número B_n de Bernoulli. Éstos se generan de x/(e^x-1)=\sum_{n\ge 0}B_n x^n/n!

Usando el "functional equation" (véase el "The Riemann Hypothesis (HD Long version)" de "rayuwish"), éste es básicamente igual que Euler' fórmula de s para la zeta(2n).

B_2 es 1/6, así que la zeta(-1) es -1/12. B_3=B_5=B_7= =0; zeta(-2)=zeta(-4) = =0.

[ortega24024]

Para encontrar donde están los otros lugares que es la zeta cero es el problema sin resolver más importante de la matemáticas.

[ortega24024]

I did graphics like this many years ago and am making some videos of my own about this stuff. My video response to this one has been there a while, but I've just put a load of comments on it trying to explain some trippy stuff, and telling stories about when I met some of the top guys on it.

[ArcaneInquisitor]

looks like a 3d version of the sin(x^2)

[1nglewattz1]

Let me see if I understand. Only the value zero functions come to the same exact points, and no other numbers?

[fenetremagique]

There are other argument values of Zeta(z) that have real part 1/2 since the domain is all complex numbers, but Riemann's hypothesis states that all the zeroes of the function must have this property. That is, if Zeta(z) = 0, then z = (1/2) + bi.

[magumslayer]

Wow. If I get this right it sounds kind of genius and idiotic at the same time.

It's not difficult to get if viewed with an open mind.

[ProsperosCloset]

Wonderous! Thank you so much!

[amjwUK]

This is an excellent explanation of the hypothesis to someone who has not got a clue about the 'Riemann zeta function' or even any knowledge above highschool level mathematics.

You should make one for P=NP and the other CMI millenium prize problems, although I have no idea if that could be done :|

[zombierobopirate]

math is beautiful

[gvsfgdf]

@zombierobopirate applied math is beautiful not pure math number theory bulshit...... Differential equations=useful..... number theory = fail

[theCamelCase]

@gvsfgdf You're grossly misinformed. Number theory is extremely important in fields like cryptanalysis, combinatorics, and probability, as well as bioinformatics and computational chemistry. It's just not as integral to physics as calculus is, if you'll forgive the pun. You should also bear in mind that, until recently, group theory was considered theoretical; now it's understood as imperative to the study of symmetry.

[ellipszia]

@zombierobopirate I agree! except when i get F in the school :D

[inglishspeeker]

wow.

well done.

[Phoenix0886]

Wonderful! How have you realized it? Which program have you used? I'm going to graduate with a thesis on Riemann Zeta, and It would be fine to create a similar video...

[pdehaye]

sorry for the late reply. i used mathematica (for the first time), version 6. i used the Manipulate instruction to move the camera to positions i wanted, then used ListInterpolation to interpolate between those different points. this generated a series of images which i then animated using a stop motion program.

[gae3tano]

@pdehaye excuse me, but i don't undestand what are the real relations between the zero's on the critical line of rienmann hypotesys and prime numbers..there's somebody who can to explain that relations!??thancks

[pdwu2]

@gae3tano The relation between the Rieman zeta function and primes is given by the Euler product formula, see wikipedia

[ortega24024]

It's easier to write your own programs than to use Mathematica (or whatever) sometimes! Hope your thesis went (or is going) OK. I did programmed zeta function graphics on an Amiga in 1993 - which ended up in a book in 2002.

[sucsmade]

wow

[ViRtUaLdJmOuSe19]

exelente