_"It has an analytical relationship to -1/12. It adds up to ♾."_ That's somewhat contradictory. ζ(-1) certainly does not "add up" to ♾. The sum Σ [k=1...∞] k _does_ add up to inifinity, but that is not ζ(-1), although it has some formal relationship to ζ(s) with Re(s)>1. It is true that the _functional equation_ can be used for analytical continuation, just as you said, and I try to rewrite that in a more (hopefully) readable form. ζ(s) = 1/π (2π)ˢ sin(πs/2) Γ(1 − s) ζ(1 − s) which may also be written equivalently as ζ(1 − s) = 2/(2π)ˢ cos(πs/2) Γ(s) ζ(s) or even symmetrically as ζ(2s) Γ(s) / πˢ = ζ(2z) Γ(z) / πᶻ with z = −s + 1/2 (or 2z = 1 - 2s).
@@ephemera2 "Nazi" being in permanent use by some people even for the pettiest incidents. I was only intending to complement this comment, not intending to criticize anybody.
It's not wrong, it's a double assignment of a variable, something which happens all the time in mathematics for convenience reasons. Since the analytic continuation is unique, it is very natural to name it also "zeta".
@@PW-qi1gi Anteater is right. I think you misunderstood their comment. They didn't argue that zeta(-1) is not -1/12, but that zeta(-1) is not 1+2+3+4+.... Yes, you can define zeta, and then define zeta as the analytic continuation of zeta (different objects, one is a subset of the other one, but we gave them the same name). But it doesn't change the definition of the sum of infinite series, thus 1+2+3+4+... still diverges to infinity, and is not equal to -1/12.
Are you a bona fide mathematician? If so, then I may have a proof of the zeta function being defined by analytic continuation for. numbers N where n < 1. Can you point me to someone who can rebut it with me?
Sir why did you use cos sine tretra hybide in this process we could have simply used zeta lite time kind equation towards solving the graph. And secondly can you please research and make a video on brother half kind equation the one introduce in 1917 needed to find more about it
Right off the bat, at approx. 0:36, I was confused. You state that the function was originally only defined for when (s) had a real part greater than 1. It seems to me that the Zeta function is perfectly well defined at (s)=1, where the function becomes 1 plus the reciprocal of the counting numbers. At (s)=0, which is certainly a real part not greater than 1, then the function becomes the infinite addition of 1+1. Hmmm, where am I going wrong?
The defining series of the zeta-function is said to be divergent for all complex numbers 1 + i*x, with x being some real number. This is clear for x=0 (harmonic series diverges) but not that clear for x ≠ 0, as now the angles of 1/n^(1+ix) are always changing: 1/n^(1+ix) = exp(-ln(n)) * exp(-i * x*ln(n)). Apparently this series does some "random walk", and although the steps are getting ever smaller (converging to zero), the series never converges. I don't know any proof of this, though.
I subscribed you! Good that I could understand the whole video, since you explained it so well! (just good amount of image description, sometimes it confuses people; just a personal thought though...)
Listen at 6:58.. I see the 60.7927.. No I see 6079 is prime. And what. Do I do. I devide by 2 3039 and +2 is a prime subtract 2 to get 3039.Devide by 3 it's a prime. .And devide by 2 again 506.5.... multiply by 36... Add 1. To see 18,207.prime.
🍎Hyper charge. The electron charge -1 is equal to -1 hypercharge. So -1=12ζ(-1). It's 12 dimensions. Quark and lepton have a total of 12. The hypercharge -1/2=-6/12=6ζ(-1) is 6th dimension. The hypercharge -1/4=3ζ(-1) is 3D. Color charge is 3D. The hypercharge -1/3=4ζ(-1) is 4th dimension. The hypercharge -5/12=5ζ(-1) is 5th dimension. Or -5/6 = 10 dimensions of 10ζ(-1). For hypercharge -70/12, -70/12= -35/6= -5×7/6= 70ζ(-1). It's 70 dimensions. The hypercharge -2/3=8ζ(-1) is 8th dimension. It's 8 gluons. The hypercharge -1/2=6ζ(-1) is 6th dimension. It's a quark lepton. The hypercharge -3/4=9ζ(-1) is 9th dimension. The hypercharge -5/6=10ζ(-1) is 10th dimension. The hypercharge -11/12=11ζ(-1) is 11 dimensions. Einstein thinks the 4th dimensional time space is 12 dimensional. The hypercharge -2=24ζ(-1) is 24th dimension. Graviton. Einstein's 4th dimensional time space is 12 dimensional. And Leech Λ24 Lattice. It's in 24th dimension. It's on the 70th dimension. The prince must kiss 196,560 times to revive the captive Snow White of Leech Λ24 Lattice. The black hole will settle to the Euler constant γ. The Arc of the Blue Sky was painted with π, and the rainbow color was painted with 3 colors of RGB, and 8 Gluons were Divided into The Heavens and Earth of The Universe. Everything is Due to The Grace of The Graviton.
Tous les explication ce ni que superficielle la question consiste de la formule général de la série ' une idée F(s)=la somme 1/n^s=la somme 1/n^a ×e^-ibln(n)=la somme 1/n^a(cosbln(n) - sinbln(n)) =
F(s)=la somme 1/n^a(cosbln(n) - isinbln(n))=la somme cosbln (n)/n^a - la somme isinbln (n)/n^a poson u(n)=la somme cosbln (n)/n^a et v(n)= isinbln(n)/n^a d ou F(s)=u(n)-iv(n) peut écrit (u(n)^2+v(n)^2)^1/2 ×e^itng(u(n)/v(n)) ' F(s)=0 équivalent (u(n)^2+v(n)^2)^1/2 tend vers 0 consiste la valeur de a réel de complex
to get an easyer expression of the Riemann-Zetafunction try Zeta (x) = 0.5 + i(e^(x+pi*pi-6)). If you put the n (element of natural numbers) as start of its Indefinite integral and n+1 as end you will get the square of the n-th prime number. This is a proof of the Riemann hypothesis. If you want another proof draw a circle with any radius >1 from the origin (0/0) then draw a complex conjunction of this [p2(0/1)] the intersections are the ony viable points and the real part is always 0.5 -> qed
You might find this useful. The answer to the Riemann Hypothesis is Infinity. Infinity times infinity equals infinity to the power of infinity. Infinity squared equals infinity to the power of infinity. If 2 is a prime then so is infinity. You are all welcome.
@@p_square All numbers are comprised of Primes but not all numbers are comprised of non-Primes. Primes make up the building blocks of infinity. They are telling the other numbers what to do. People are looking at numbers and infinity incorrectly. Infinity is Prime so case closed on the Hypothesis. all the non-zeros have the same point of origin as does infinity so all of them are going to be in the same place just on an endless line. You are never going to find one that doesn’t share this behavior with every other prime.
Gauss discovered that 1+2+3+...+n=(n+1)*n/2 when he was 8! = 40320 years old
😁
😂
Zeta (-1) does not "add up to" -1/12. It has an analytical relationship to -1/12. It adds up to ♾️. For the Riemann Zeta function, when dealing with n
_"It has an analytical relationship to -1/12. It adds up to ♾."_
That's somewhat contradictory. ζ(-1) certainly does not "add up" to ♾.
The sum Σ [k=1...∞] k _does_ add up to inifinity, but that is not ζ(-1), although it has some formal relationship to ζ(s) with Re(s)>1. It is true that the _functional equation_ can be used for analytical continuation, just as you said, and I try to rewrite that in a more (hopefully) readable form.
ζ(s) = 1/π (2π)ˢ sin(πs/2) Γ(1 − s) ζ(1 − s)
which may also be written equivalently as
ζ(1 − s) = 2/(2π)ˢ cos(πs/2) Γ(s) ζ(s)
or even symmetrically as
ζ(2s) Γ(s) / πˢ = ζ(2z) Γ(z) / πᶻ
with z = −s + 1/2 (or 2z = 1 - 2s).
@@miloszforman6270 You wanna be a grammar nazi go ahead. Add up to infinity; diverges to infinity. You know what I meant
@@ephemera2
"Nazi" being in permanent use by some people even for the pettiest incidents. I was only intending to complement this comment, not intending to criticize anybody.
@@miloszforman6270 apologies
@miloszforman6270 wait. Random question. You aren't, by any chance, a geologist or archeologist r u?
Euler enter the room
Solve the basel problem
Leaves.
CHADEST MATHEMATICIAN
Great Video!!!
10:00 that’s not what zeta(-1) is. Zeta is defined only by analytic continuation for Re(s)
Agree. It is not correct that statement.
It's not wrong, it's a double assignment of a variable, something which happens all the time in mathematics for convenience reasons. Since the analytic continuation is unique, it is very natural to name it also "zeta".
@@PW-qi1gi It is wrong. zeta(-1) is not the sum of the natural numbers.
@@PW-qi1gi Anteater is right. I think you misunderstood their comment. They didn't argue that zeta(-1) is not -1/12, but that zeta(-1) is not 1+2+3+4+.... Yes, you can define zeta, and then define zeta as the analytic continuation of zeta (different objects, one is a subset of the other one, but we gave them the same name). But it doesn't change the definition of the sum of infinite series, thus 1+2+3+4+... still diverges to infinity, and is not equal to -1/12.
@@tgr5588 Aha, I misunderstood the comment.
Would you have any advice on my zeta function? Transcendental Zeta Function
Are you a bona fide mathematician? If so, then I may have a proof of the zeta function being defined by analytic continuation for. numbers N where n < 1. Can you point me to someone who can rebut it with me?
Buen video👍👍👍👍
Sir why did you use cos sine tretra hybide in this process we could have simply used zeta lite time kind equation towards solving the graph. And secondly can you please research and make a video on brother half kind equation the one introduce in 1917 needed to find more about it
May I ask why Euler started with sin x?
Love you BRO , your vedio helped me to complete my research
I’m glad you found it helpful!
Right off the bat, at approx. 0:36, I was confused. You state that the function was originally only defined for when (s) had a real part greater than 1. It seems to me that the Zeta function is perfectly well defined at (s)=1, where the function becomes 1 plus the reciprocal of the counting numbers. At (s)=0, which is certainly a real part not greater than 1, then the function becomes the infinite addition of 1+1. Hmmm, where am I going wrong?
I believe, relying on others who know more than me, that the Zeta function converges only when s>1. Is that what you meant?
1 + 1/2 + 1/3 + ... diverges
Any input
The defining series of the zeta-function is said to be divergent for all complex numbers 1 + i*x, with x being some real number. This is clear for x=0 (harmonic series diverges) but not that clear for x ≠ 0, as now the angles of 1/n^(1+ix) are always changing: 1/n^(1+ix) = exp(-ln(n)) * exp(-i * x*ln(n)). Apparently this series does some "random walk", and although the steps are getting ever smaller (converging to zero), the series never converges. I don't know any proof of this, though.
cool video
fantastic!
I subscribed you! Good that I could understand the whole video, since you explained it so well! (just good amount of image description, sometimes it confuses people; just a personal thought though...)
nice profile picture
This video is good and you should feel good
Thank you :D
Ryan why did your Calc BC final project end up getting thousands of views?
I have no idea hahahaha
Wait this was his calculus final project haha I'm studying riemann zeta function for my school project in 6th grade
Listen at 6:58..
I see the 60.7927..
No I see 6079 is prime.
And what. Do I do.
I devide by 2 3039 and +2 is a prime subtract 2 to get 3039.Devide by 3 it's a prime. .And devide by 2 again 506.5.... multiply by 36... Add 1. To see 18,207.prime.
That is Madhava series
Riemann zeta function is convergent or divergent
yes
What is x?
x can be any number as needed .
🍎Hyper charge.
The electron charge -1 is equal to -1 hypercharge.
So -1=12ζ(-1). It's 12 dimensions.
Quark and lepton have a total of 12.
The hypercharge -1/2=-6/12=6ζ(-1) is 6th dimension.
The hypercharge -1/4=3ζ(-1) is 3D.
Color charge is 3D.
The hypercharge -1/3=4ζ(-1) is 4th dimension.
The hypercharge -5/12=5ζ(-1) is 5th dimension.
Or -5/6 = 10 dimensions of 10ζ(-1).
For hypercharge -70/12,
-70/12=
-35/6=
-5×7/6=
70ζ(-1).
It's 70 dimensions.
The hypercharge -2/3=8ζ(-1) is 8th dimension.
It's 8 gluons.
The hypercharge -1/2=6ζ(-1) is 6th dimension.
It's a quark lepton.
The hypercharge -3/4=9ζ(-1) is 9th dimension.
The hypercharge -5/6=10ζ(-1) is 10th dimension.
The hypercharge -11/12=11ζ(-1) is 11 dimensions. Einstein thinks
the 4th dimensional time space is 12 dimensional.
The hypercharge -2=24ζ(-1) is 24th dimension. Graviton.
Einstein's 4th dimensional time space is
12 dimensional.
And Leech Λ24 Lattice.
It's in 24th dimension.
It's on the 70th dimension.
The prince must kiss
196,560 times to revive
the captive Snow White of Leech Λ24 Lattice.
The black hole will settle to the Euler constant γ.
The Arc of the Blue Sky was painted with π,
and
the rainbow color was painted with 3 colors of RGB,
and
8 Gluons were Divided into
The Heavens and Earth of
The Universe.
Everything is Due to The Grace of The Graviton.
Tous les explication ce ni que superficielle la question consiste de la formule général de la série ' une idée F(s)=la somme 1/n^s=la somme 1/n^a ×e^-ibln(n)=la somme 1/n^a(cosbln(n) - sinbln(n)) =
F(s)=la somme 1/n^a(cosbln(n) - isinbln(n))=la somme cosbln (n)/n^a - la somme isinbln (n)/n^a poson u(n)=la somme cosbln (n)/n^a et v(n)= isinbln(n)/n^a d ou F(s)=u(n)-iv(n) peut écrit (u(n)^2+v(n)^2)^1/2 ×e^itng(u(n)/v(n)) ' F(s)=0 équivalent (u(n)^2+v(n)^2)^1/2 tend vers 0 consiste la valeur de a réel de complex
to get an easyer expression of the Riemann-Zetafunction try Zeta (x) = 0.5 + i(e^(x+pi*pi-6)). If you put the n (element of natural numbers) as start of its Indefinite integral and n+1 as end you will get the square of the n-th prime number. This is a proof of the Riemann hypothesis. If you want another proof draw a circle with any radius >1 from the origin (0/0) then draw a complex conjunction of this [p2(0/1)] the intersections are the ony viable points and the real part is always 0.5 -> qed
Bread 👍
zeta riemann P prime
What
@@ryan2-518 kim raisner
If education plugged your brain in and the educated plugged a computers brain in,then the question is can either parties answer it?
1:20
#Jargon
It’s a problem that you have to read up on a lot about.
Poggers
I might be wrong, but this could work: ua-cam.com/video/PvUrbpsXZLU/v-deo.html
P.S. A piece of advice: make video 1.5 faster, I speak very slowly)
0
Hi This is Abhijeet Deshpande and....
This is how to understand the theorem....
Points:
1.) From 1 to 100, calculate the number of odds and evens
2.) Now for every single of the odd and even numbers, measure and write down the number of steps, for both to go to the number 4.
3.) For both the odd and even numbers, calculate individually as below,
a.) Add the number of steps to get a total of both odd and even
b.) Get a total of odd / even numbers by addition
i.e.
a.) How many numbers are odd and even
b.) And what the the sum total of odd and even by addition
c.) What is the sum total of odd and even by division
d.) What is the sum total of odd and even numbers by substraction
4.) Divide the number of steps with the number of odd / even numbers wiithin 1 to 100
5.) Now upon fiding the value of the division of both odd and even numbers,
Use the above results of calculations to calculate with the results to determine the base structure or the point of average c
divisions or calculations, where both the calculations of odd and even align,
And Voila, you have a symmetry of calculative set of equations that would determine the results of any similar supposedly unsolvable equations.
These equative calculations of mine can also solve the problems of Rieman hypothesis of prime numbers as well.
As such I am eligible to win the seed of Clay Institute for of and towards the same.
3x+1, Rieman Hypothesis
© Abhijeet Deshpande, 2021
Thank
submit this to the CMI and they wont even take a minute to reject this :D
E
RiemaNN please!
😂😂😂
You might find this useful.
The answer to the Riemann Hypothesis is Infinity.
Infinity times infinity equals infinity to the power of infinity.
Infinity squared equals infinity to the power of infinity.
If 2 is a prime then so is infinity.
You are all welcome.
not rigorous
@@p_square All numbers are comprised of Primes but not all numbers are comprised of non-Primes. Primes make up the building blocks of infinity. They are telling the other numbers what to do. People are looking at numbers and infinity incorrectly. Infinity is Prime so case closed on the Hypothesis.
all the non-zeros have the same point of origin as does infinity so all of them are going to be in the same place just on an endless line. You are never going to find one that doesn’t share this behavior with every other prime.
@@alexanderealley9992 You are spewing nonsense
Dumb.
हिंदी में समझाओ plz
Ya, it's much easier to win $1M than to solve a math problem.
U don't know what u say, you are just reading