Staredit Network

If any of you can prove (or disprove) the Riemann Hypothesis, you are entitled to $1 million and will be famous in the process...this hypothesis been around for around 150 years, unproven

here is the hypothesis

Sorry bout the dark picture, black doesn't do well on the dark green SEN background


---------------------



It has to do with the Riemann Zeta function, so first off i will tell you what the zeta function is...


for s a complex number. This function is analytic for real part of s greater than 1 and is related to the prime numbers by the Euler Product Formula



again defined for real part of s greater than one. This function extends to points with real part s less than or equal to one by the formula (among others)



The contour here is meant to indicate a path which begins at positive infinity, descends parallel to and just above the real axis, circles the origin once in the counterclockwise direction, and then returns to positive infinity parallel to and just below the real axis. This function is analytic at all points of the complex plane except the point s = 1 where it has a simple pole. This last function is the Riemann Zeta Function (the zeta function).



Now the Riemann Hypothesis

The zeta function has no zeros in the region where the real part of s is greater than or equal to one. In the region with real part of s less than or equal to zero the zeta function has zeros at the negative even integers; these are known as the trivial zeros. All remaining zeros lie in the strip where the real part of s is strictly between 0 and 1 (the critical strip). It is known that there are infinitely many zeros on the line 1/2 + it as t ranges over the real numbers. This line in the complex plane is known as the critical line. The Riemann Hypothesis (RH) is that all non-trivial zeros of the zeta function lie on the critical line. Let's say that again:

Riemann Hypothesis:
all non-trivial zeros of the zeta function lie on the line 1/2 + it as t ranges over the real numbers.

-----------------------------


I would be very impressed if you proved/disproved this, and you would win one million dollars

I doubt anyone would put it here, they'd go get the mil first.

I already did this thread, DTBK said that he could, but didn't feel like it.

He didn't feel like doing something that would get him a million dollars= he doesn't know.

I highly doubt, no, I know for a fact that nobody here can disprove Riemann's hypothesis.

The basic mathematics behind Riemann's work in order to understand it is at least Calculus III, according to my text-book, something that only Engineers, Physicists and Mathematicians study. (Not sure if Chemists also study it) In order to disprove this, you certainly need to know Ordinary Differential Equations since it is describing a function and it's graph. I also wouldn't doubt if you needed Analytical Differential Equations in order to go forward and backwards in providing the proof for this. These courses are only given in a few University degrees.

DTBK said he could do it? o rly?

That they do.

Well he said he knew how, but he wouldn't bother trying.

He may have a general concept on a possible alternative to the hypothesis, but I doubt that he could disprove Riemann. Not saying that Riemann is right/wrong, just saying that nobody here on SeN can actually mathematically prove it in a correct manner.

A concept is one thing, proof is another. If I studied that basis of zeta functions and Riemann's hypothesis, I may come up with an idea, but I couldn't even prove my own idea in the first place. Disproving something that many mathematicians have accepted is another thing.

Reminds me of how Einstein disproved Newton's definition of how gravity works.

You said something of the sort, but I misphrased it.

http://www.staredit.net/index.php?showtopi...ndpost&p=583480

You said you knew what it meant, and you wouldn't try. Not you could but you wouldn't try. It was 2 months ago, and therefor not long enough to really sink in.