Riemann hypothesis Definition and 74 Threads

I have two questions: Why hasn't the hypothesis been proved yet? Is it because we don't know why re(s) has to be 1/2 and thus can't prove it, or is it because we know why re(s) has to be 1/2 but we just don't know how to prove it. Why exactly does re(s) have to be 1/2? \zeta...

I have a question concerning the Riemann Hypothesis, a conjecture about the distribution of zeros of the Riemann-zeta function. the trivial zeros (s=-2, s= -4, s=-6) arent much of a concern as the NON-trivial zeros, where any real part of the non-trivial zero is = 1/2. What i am having...

Lagarias’ equivalence to the Riemann hypothesis should be discussed, i.e., if hn := n-th harmonic number := 1/1 + 1/2 + · · · + 1/n, and σn := divisor function of n := sum of positive divisors of n, then if n > 1, hn + ehn ln hn > σn. There is a $1,000,000 prize for the proof of this at...

http://arxiv.org/abs/0806.0892"

i am a high school student i want to prove the riemann hypothesis but i do not how to start:confused:

Can somebody explain me about the trivial zeros? Why \zeta(-2) = \zeta(-4) = \zeta(-6) = 0 = \zeta(k) So \zeta(k) \sum_{n=1}^{ \infty} \frac{1}{n^k} = 0 ?

http://www.arsmathematica.net/archives/2007/05/22/latest-on-latest-paper-on-arxiv/

Can someone please explain to what exactly the Riemann Hypothesis is? My friend said it is something to do with imaginary numbers and how they behave in a certain interval- just wondering.

Let H_{n}=\sum_{k=1}^{n}\frac{1}{k} be the nth harmonic number, then the Riemann hypothesis is equivalent to proving that for each n\geq 1, \sum_{d|n}d\leq H_{n}+\mbox{exp}(H_{n})\log H_{n} where equality holds iff n=1. The paper that this came from is here: An Elementary Problem...

let \zeta(z)=\sum_{n \in \mathbb{N}} n^{-z} ~ {{a+ib}}>1 then, \zeta(z)=0 iff z=-2n where n is a natural number. pi(x)=\int_0^\infty\frac{dx}{\xS[x+1]} gamma(x+) where S[x+1]= \sum_{n \in \mathbb{N}} n^-{x+1} I have discovered that pi(x)=\int_a^b\frac{dx}/logx = 1/log b+ 2/log b...

Just wondering if any of the posters seriously tried solving Riemann Hypothesis. And if yes, then what kinds of problems did you run into?

I know this is one of the famous unsolved problems still hanging around. Could someone give me the "gist" of it, and what the implications are if it is solved one way or the other? I looked it up on Wikipedia but that didn't help me much. Has anyone any idea why it is so hard to solve (i imagine...

Heilbronn proved that the Epstein Zeta function did not satisfy RH...but the Zeta function \zeta(s) can be put in a form of an Epstein function but a factor k..let be the functional equation for Epstein functions: \pi^{-s}\Gamma(s)Z_{Q^{-1}}(s)=|Q|^{1/2}\pi^{s-n/2}\Gamma(n/2-s)Z_{Q}(n/2-s)...

to publish it because i,m not a famous teacher,mathematician from a snob and pedant univesity of Usa of England...this is the way science improves..only by publishing works from famous mathematician..:mad: :mad: :mad: :mad: :mad: o fcourse if i were Louis de Branges or Alain Connes or other...

I've tried my best to understand the Riemann Zeta Function on my own, but I appeal to the knowledge of you guys to help me understand more. For s >1 , the Riemann Zeta Fuction is defined as: \zeta(s)=\sum_{n=1}^{\infty}n^{-s} I have no problem with this. That series obviously converges...

this is a question i have i mean are RH and Goldbach conjecture related? i mean in the sense that proving RH would imply Goldbach conjecture and viceversa: RIemann hypothesis: (RH) \zeta(s)=0 then s=1/2+it Goldbach conjecture,let be n a positive integer then: 2n=p1+p2 ...

Let be the Hamitonian of a particle with mass m in the form: H=\frac{-\hbar^{2}}{2m}D^{2}\phi(x)+V(x)\phi(x) then the RH is equivalent to prove that exist a real potential V(x) of the Hamiltonian so that the values E_n H\phi=E_{n}\phi satisfy the equation \zeta(1/2+iE_{n})=0 that is...

What would be the effects on the world and to the individual or individuals if the Riemann Hypothesis was solved?

Hi, When I hear about the Riemann hypothesis, it seems like the first thing I hear about it is its importance to the distribution of prime numbers. However, looking online this seems to be a very difficult thing to explain. I understand that the Riemann Hypothesis asserts that the zeroes of...

hello all after doing a bit of research on the riemann hypothesis I came along this paragraph, in which I don't understand, especially the first sentence , how would one be able to show that? It can be shown that \zeta (s) = 0 when s is a negative even integer. The famous Riemann...

http://news.uns.purdue.edu/UNS/html4ever/2004/040608.DeBranges.Riemann.html Any news since then? There are links to the papers themselves on the bottom of the page. But I can't understand much, I'm afraid.

In June of this year the mathematician Louis de Branges published in Internet a proposed "proof" of the Riemann Hypothesis. The page is: http://www.math.purdue.edu/~branges/riemannzeta.pdf Years ago De Branges proved the Bieberbach Conjecture. He has tried several times to proof the RH...

Just an opinion question, do you think that the riemann hypothesis will ever be proven? If so, how long do you think it will take?

What is the Riemann Hypothesis? Where can I find good online literature upon the subject?:smile: