The Riemann hypothesis

[matrixscarface]

Does anyone know abou the "riemann hypothesis" and/or "the riemann zeta function"?? i hear tell that claymath put a million dollar reward on whoever could solve it among other problems but... what is it????

[Tormod]

The Riemann hypothesis is a mathematical puzzle.

 

There are actually many of them, but I assume you mean the one that is derived from the prime number theorem.

 

There is some info here:

http://mathworld.wolfram.com/RiemannZetaFunction.html

[matrixscarface]

i have been here, but what does this all mean?? and what other ones?

[Bo]

in genberal a zeta function is a function of the form: f(s) = sum (n=0 to inf) g(n)^(-s)

the Rieman zeta function isgiven by: f(s)= sum(n=0 to inf) n^(-s). So for example: f(2)=0+1^(-2)+2^(-2)+3^(-2)+... etc. Zeta functions are extremely important especially in number theorem (the function f(s) is related to the number of prime's smaller then s) and it can be used to solve certain integrals.

The riemann hypothesis is that the euation f(s)=0, holds if the real part of s is 1/2.

I hope this is more clear.

 

Bo

[matrixscarface]

i still don't get it, i didn't understand a word you just said. please explain this in a simple term i wanna solve it.. help the curious

[Tormod]

matrix, if you want to solve the Riemann hypothesis you probably need to understand what Bo just wrote. :naughty:

 

I read a good book last summer about the RH:

 

Marcus du Sautoy

The music of the Primes: Searching to solve the greatest mystery in mathematics

 

http://www.hypography.com/amazon_detail.cfm?asin=0066210704

 

Highly recommended.

[Bo]

like tormod said: if you diddn't understood my post you will have a very hard time proving the riemann hypothesis (remember that this is a problem where in the past century the smartest mathematiciens in the world have worked on...)

 

Well let's see if i can be more clearly:

the Rieman zeta function isgiven by: f(s)= sum(n=0 to inf) n^(-s).

 

so this is a function f, that depends on some complex number s (complex numbers are numbers with a real and an imaginary component). This function is given by an infinite sum n^(-s) (^means 'to the power of'). so the first components of this sum are:

n=0 --> 0^(-s) =0

n=1 --> 1^(-s)

n=2 --> 2^(-s)

etc.

so f(s) is given by 0+1^(-s)+2^(-s)+.... etc until infinity.

 

The riemann hypothesis is that the euation f(s)=0, holds if the real part of s is 1/2.

 

Bo