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dylanbuider is not online. dylanbuider
Joined: 14 Jun 2008
Total Posts: 17141
04 Mar 2012 11:20 AM
I'm serious. No joking here, even though it's outrageous.


To get the R$:

Make a correct proof Riemann Hypothesis.
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RY84TTT is not online. RY84TTT
Joined: 21 Jul 2011
Total Posts: 13781
04 Mar 2012 11:21 AM
Im only in 7th grade hnrs and I'm pretty sure thats high school.
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townbuilder825 is not online. townbuilder825
Joined: 11 Aug 2008
Total Posts: 24571
04 Mar 2012 11:21 AM
Lol, that's worth more then 1mil robux
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DarkGenex is not online. DarkGenex
Joined: 11 Feb 2010
Total Posts: 44785
04 Mar 2012 11:21 AM
The Riemann hypothesis implies that the zeros of the zeta function form a quasicrystal, meaning a distribution with discrete support whose Fourier transform also has discrete support. We can make proof of it by classifying, or at least studying, 1-dimensional quasicrystals.
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Papaluty is not online. Papaluty
Joined: 13 May 2011
Total Posts: 15076
04 Mar 2012 11:22 AM
Is this like your science homework project? x3

**~Moo~**
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joshiscool22222 is not online. joshiscool22222
Joined: 27 May 2010
Total Posts: 29029
04 Mar 2012 11:22 AM
I would, but I dislike math even though I learned this. I forgot most of it.
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TheBankingVault is not online. TheBankingVault
Joined: 19 Feb 2011
Total Posts: 15161
04 Mar 2012 11:22 AM
Internet ftw

"i m r noob, ogm, so r u" ~Teh Banking of Vaults
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IRobbedTheBank is not online. IRobbedTheBank
Joined: 04 Feb 2012
Total Posts: 1320
04 Mar 2012 11:22 AM
have no zeros when the real part of s is greater than one then
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RY84TTT is not online. RY84TTT
Joined: 21 Jul 2011
Total Posts: 13781
04 Mar 2012 11:22 AM
f
l
o
o
d
c







The real part (red) and imaginary part (blue) of the Riemann zeta function along the critical line Re(s) = 1/2. The first non-trivial zeros can be seen at Im(s) = ±14.135, ±21.022 and ±25.011.


Millennium Prize Problems



P versus NP problem



Hodge conjecture



Poincaré conjecture



Riemann hypothesis



Yang–Mills existence and mass gap



Navier–Stokes existence and smoothness



Birch and Swinnerton-Dyer conjecture




v ·
t ·
e


In mathematics, the Riemann hypothesis, proposed by Bernhard Riemann (1859), is a conjecture about the location of the nontrivial zeros of the Riemann zeta function which states that all non-trivial zeros (as defined below) have real part 1/2. The name is also used for some closely related analogues, such as the Riemann hypothesis for curves over finite fields.
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DriftSpeed is not online. DriftSpeed
Joined: 30 May 2009
Total Posts: 6836
04 Mar 2012 11:22 AM
Ogm dark can copy paste
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dylanbuider is not online. dylanbuider
Joined: 14 Jun 2008
Total Posts: 17141
04 Mar 2012 11:22 AM
@dark

that was a failed one

>fail
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Papaluty is not online. Papaluty
Joined: 13 May 2011
Total Posts: 15076
04 Mar 2012 11:23 AM
In mathematics, the Riemann hypothesis, proposed by Bernhard Riemann (1859), is a conjecture about the location of the nontrivial zeros of the Riemann zeta function which states that all non-trivial zeros (as defined below) have real part 1/2. The name is also used for some closely related analogues, such as the Riemann hypothesis for curves over finite fields.
The Riemann hypothesis implies results about the distribution of prime numbers that are in some ways as good as possible. Along with suitable generalizations, it is considered by some mathematicians to be the most important unresolved problem in pure mathematics (Bombieri 2000). The Riemann hypothesis is part of Problem 8, along with the Goldbach conjecture, in Hilbert's list of 23 unsolved problems, and is also one of the Clay Mathematics Institute Millennium Prize Problems. Since it was formulated, it has remained unsolved.
The Riemann zeta function ζ(s) is defined for all complex numbers s ≠ 1. It has zeros at the negative even integers (i.e. at s = −2, −4, −6, ...). These are called the trivial zeros. The Riemann hypothesis is concerned with the non-trivial zeros, and states that:
The real part of any non-trivial zero of the Riemann zeta function is 1/2.

XDXDXDXD I WUV U G00GLE!!! XDXDXDXDXD

~Moo~
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akaboom3 is not online. akaboom3
Joined: 07 Oct 2010
Total Posts: 12449
04 Mar 2012 11:25 AM
that theory had not been solved by a dude using 10 years of his life..
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funnynon is not online. funnynon
Joined: 10 Jun 2009
Total Posts: 14975
04 Mar 2012 11:26 AM
I searched that on google, then i looked at the previous tab, and it said "Pokememes"

derp
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ProLMaDer is not online. ProLMaDer
Joined: 24 Feb 2012
Total Posts: 342
04 Mar 2012 11:26 AM
where λ(n) is the Liouville function given by (−1)r if n has r prime factors. He showed that this in turn would imply that the Riemann hypothesis is true. However Haselgrove (1958) proved that T(x) is negative for infinitely many x (and also disproved the closely related Pólya conjecture), and Borwein, Ferguson & Mossinghoff (2008) showed that the smallest such x is 72185376951205. Spira (1968) showed by numerical calculation that the finite Dirichlet series above for N=19 has a zero with real part greater than 1. Turán also showed that a somewhat weaker assumption, the nonexistence of zeros with real part greater than 1+N−1/2+ε for large N in the finite Dirichlet series above, would also imply the Riemann hypothesis, but Montgomery (1983) showed that for all sufficiently large N these series have zeros with real part greater than 1 + (log log N)/(4 log N). Therefore, Turán's result is vacuously true and cannot be used to help prove the Riemann hypothesis.
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xCOMPLETEx is not online. xCOMPLETEx
Joined: 24 Dec 2011
Total Posts: 17517
04 Mar 2012 11:26 AM
@RY84TTT

7th grade IS high school...
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Papaluty is not online. Papaluty
Joined: 13 May 2011
Total Posts: 15076
04 Mar 2012 11:27 AM
nomeh
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dylanbuider is not online. dylanbuider
Joined: 14 Jun 2008
Total Posts: 17141
04 Mar 2012 11:27 AM
"Turán's result is vacuously true and cannot be used to help prove the Riemann hypothesis. "

xD ufail
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joshiscool22222 is not online. joshiscool22222
Joined: 27 May 2010
Total Posts: 29029
04 Mar 2012 11:27 AM
No proof has come yet, most have failed.
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bigpike54 is not online. bigpike54
Joined: 19 Aug 2009
Total Posts: 7960
04 Mar 2012 11:27 AM
That is virtually almost impossible.
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Papaluty is not online. Papaluty
Joined: 13 May 2011
Total Posts: 15076
04 Mar 2012 11:28 AM
Several analogues of the Riemann hypothesis have already been proved. The proof of the Riemann hypothesis for varieties over finite fields by Deligne (1974) is possibly the single strongest theoretical reason in favor of the Riemann hypothesis. This provides some evidence for the more general conjecture that all zeta functions associated with automorphic forms satisfy a Riemann hypothesis, which includes the classical Riemann hypothesis as a special case. Similarly Selberg zeta functions satisfy the analogue of the Riemann hypothesis, and are in some ways similar to the Riemann zeta function, having a functional equation and an infinite product expansion analogous to the Euler product expansion. However there are also some major differences; for example they are not given by Dirichlet series. The Riemann hypothesis for the Goss zeta function was proved by Sheats (1998). In contrast to these positive examples, however, some Epstein zeta functions do not satisfy the Riemann hypothesis, even though they have an infinite number of zeros on the critical line (Titchmarsh 1986). These functions are quite similar to the Riemann zeta function, and have a Dirichlet series expansion and a functional equation, but the ones known to fail the Riemann hypothesis do not have an Euler product and are not directly related to automorphic representations.
The numerical verification that many zeros lie on the line seems at first sight to be strong evidence for it. However analytic number theory has had many conjectures supported by large amounts of numerical evidence that turn out to be false. See Skewes number for a notorious example, where the first exception to a plausible conjecture related to the Riemann hypothesis probably occurs around 10316; a counterexample to the Riemann hypothesis with imaginary part this size would be far beyond anything that can currently be computed. The problem is that the behavior is often influenced by very slowly increasing functions such as log log T, that tend to infinity, but do so so slowly that this cannot be detected by computation. Such functions occur in the theory of the zeta function controlling the behavior of its zeros; for example the function S(T) above has average size around (log log T)1/2 . As S(T) jumps by at least 2 at any counterexample to the Riemann hypothesis, one might expect any counterexamples to the Riemann hypothesis to start appearing only when S(T) becomes large. It is never much more than 3 as far as it has been calculated, but is known to be unbounded, suggesting that calculations may not have yet reached the region of typical behavior of the zeta function.
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Papaluty is not online. Papaluty
Joined: 13 May 2011
Total Posts: 15076
04 Mar 2012 11:29 AM
x3
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choochoo322 is not online. choochoo322
Joined: 22 Jun 2009
Total Posts: 9520
04 Mar 2012 11:29 AM
where λ(n) is the Liouville function given by (−1)r if n has r prime factors. He showed that this in turn would imply that the Riemann hypothesis is true. However Haselgrove (1958) proved that T(x) is negative for infinitely many x (and also disproved the closely related Pólya conjecture), and Borwein, Ferguson & Mossinghoff (2008) showed that the smallest such x is 72185376951205. Spira (1968) showed by numerical calculation that the finite Dirichlet series above for N=19 has a zero with real part greater than 1. Turán also showed that a somewhat weaker assumption, the nonexistence of zeros with real part greater than 1+N−1/2+ε for large N in the finite Dirichlet series above, would also imply the Riemann hypothesis, but Montgomery (1983) showed that for all sufficiently large N these series have zeros with real part greater than 1 + (log log N)/(4 log N). Therefore, Turán's result is vacuously true and cannot be used to help prove the Riemann hypothesis

In mathematics, the Riemann hypothesis, proposed by Bernhard Riemann (1859), is a conjecture about the location of the nontrivial zeros of the Riemann zeta function which states that all non-trivial zeros (as defined below) have real part 1/2. The name is also used for some closely related analogues, such as the Riemann hypothesis for curves over finite fields.
The Riemann hypothesis implies results about the distribution of prime numbers that are in some ways as good as possible. Along with suitable generalizations, it is considered by some mathematicians to be the most important unresolved problem in pure mathematics (Bombieri 2000). The Riemann hypothesis is part of Problem 8, along with the Goldbach conjecture, in Hilbert's list of 23 unsolved problems, and is also one of the Clay Mathematics Institute Millennium Prize Problems. Since it was formulated, it has remained unsolved.
The Riemann zeta function ζ(s) is defined for all complex numbers s ≠ 1. It has zeros at the negative even integers (i.e. at s = −2, −4, −6, ...). These are called the trivial zeros. The Riemann hypothesis is concerned with the non-trivial zeros, and states that:
The real part of any non-trivial zero of the Riemann zeta function is 1/2.
Several analogues of the Riemann hypothesis have already been proved. The proof of the Riemann hypothesis for varieties over finite fields by Deligne (1974) is possibly the single strongest theoretical reason in favor of the Riemann hypothesis. This provides some evidence for the more general conjecture that all zeta functions associated with automorphic forms satisfy a Riemann hypothesis, which includes the classical Riemann hypothesis as a special case. Similarly Selberg zeta functions satisfy the analogue of the Riemann hypothesis, and are in some ways similar to the Riemann zeta function, having a functional equation and an infinite product expansion analogous to the Euler product expansion. However there are also some major differences; for example they are not given by Dirichlet series. The Riemann hypothesis for the Goss zeta function was proved by Sheats (1998). In contrast to these positive examples, however, some Epstein zeta functions do not satisfy the Riemann hypothesis, even though they have an infinite number of zeros on the critical line (Titchmarsh 1986). These functions are quite similar to the Riemann zeta function, and have a Dirichlet series expansion and a functional equation, but the ones known to fail the Riemann hypothesis do not have an Euler product and are not directly related to automorphic representations.
The numerical verification that many zeros lie on the line seems at first sight to be strong evidence for it. However analytic number theory has had many conjectures supported by large amounts of numerical evidence that turn out to be false. See Skewes number for a notorious example, where the first exception to a plausible conjecture related to the Riemann hypothesis probably occurs around 10316; a counterexample to the Riemann hypothesis with imaginary part this size would be far beyond anything that can currently be computed. The problem is that the behavior is often influenced by very slowly increasing functions such as log log T, that tend to infinity, but do so so slowly that this cannot be detected by computation. Such functions occur in the theory of the zeta function controlling the behavior of its zeros; for example the function S(T) above has average size around (log log T)1/2 . As S(T) jumps by at least 2 at any counterexample to the Riemann hypothesis, one might expect any counterexamples to the Riemann hypothesis to start appearing only when S(T) becomes large. It is never much more than 3 as far as it has been calculated, but is known to be unbounded, suggesting that calculations may not have yet reached the region of typical behavior of the zeta function.
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choochoo322 is not online. choochoo322
Joined: 22 Jun 2009
Total Posts: 9520
04 Mar 2012 11:30 AM
The Riemann zeta function is defined for complex s with real part greater than 1 by the absolutely convergent infinite series


Leonhard Euler showed that this series equals the Euler product


where the infinite product extends over all prime numbers p, and again converges for complex s with real part greater than 1. The convergence of the Euler product shows that ζ(s) has no zeros in this region, as none of the factors have zeros.

The Riemann hypothesis discusses zeros outside the region of convergence of this series, so it needs to be analytically continued to all complex s. This can be done by expressing it in terms of the Dirichlet eta function as follows. If s is greater than one, then the zeta function satisfies


However, the series on the right converges not just when s is greater than one, but more generally whenever s has positive real part. Thus, this alternative series extends the zeta function from Re(s) > 1 to the larger domain Re(s) > 0, excluding the zeros of (see Dirichlet eta function).

In the strip 0 < Re(s) < 1 the zeta function also satisfies the functional equation


One may then define ζ(s) for all remaining nonzero complex numbers s by assuming that this equation holds outside the strip as well, and letting ζ(s) equal the right-hand side of the equation whenever s has non-positive real part. If s is a negative even integer then ζ(s) = 0 because the factor sin(πs/2) vanishes; these are the trivial zeros of the zeta function. (If s is a positive even integer this argument does not apply because the zeros of sin are cancelled by the poles of the gamma function as it takes negative integer arguments.) The value ζ(0) = −1/2 is not determined by the functional equation, but is the limiting value of ζ(s) as s approaches zero. The functional equation also implies that the zeta function has no zeros with negative real part other than the trivial zeros, so all non-trivial zeros lie in the critical strip where s has real part between 0 and 1.
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dylanbuider is not online. dylanbuider
Joined: 14 Jun 2008
Total Posts: 17141
04 Mar 2012 11:31 AM
"It is never much more than 3 as far as it has been calculated, but is known to be unbounded, suggesting that calculations may not have yet reached the region of typical behavior of the zeta function.'

>therefore failed proof also
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