Riemann Definition and 586 Threads

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...

Please Help... Riemann Please Help! To compute the Riemann integral of f:[0,1]->R given f(x)=x^k where k>1 is an integer 1. Let m>2 and define q_m= m^(-1/m) Let P_m be the partition of [0,1] given by P_m=(0< q_m^m < q_m^(m-1)< ...< q_m <1) Explicitly evalute L(f,P_m) and U(f,P_m) 2. Show...

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)...

So it is well-known that for n=2,3,... the following equation holds \zeta(n)=\int_{x_{n}=0}^{1}\int_{x_{n-1}=0}^{1}\cdot\cdot\cdot\int_{x_{1}=0}^{1}\left(\frac{1}{1-\prod_{k=1}^{n}x_{k}}\right)dx_{1}\cdot\cdot\cdot dx_{n-1}dx_{n} My question is how can this relation be extended to...

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...

let f(x) = 1 when x in in [0,1) f(x) = -1/2 when x is in [1,2) f(x) = 1/3 when x is in [2, 3) and so on, in othe words its the sequence (1/n)(-1)^n, whose series obviously converges to log 2. However is f(x) Riemann integrable and equal to this series? If so, how to give an...

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...

Summary of the classical proof by Riemann and Roch Let D = p1 + ...+pd be a divisor of distinct points on a compact connected Riemann surface X of genus g, and let L(D) be the space of meromorphic functions on X with at worst simple poles contained in the set {p1,...,pd}. For each point pj...

let be the quotient: Lim_{x->c}\frac{\zeta(1-x)}{\zeta(x)} where x=c is a root of riemann function... then my question is if that limit is equal to exp(ik) with k any real constant...thanks... the limit is wehn x tends to c bieng c a root of riemann constant

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 well I was working through Riemanns Criterion : let f be a bounded function on the closed interval [a,b]. then f is riemann integrable on [a,b] if and only if , given any epsilon>0, there exist a partition P of [a,b] such that U(f,P)-L(f,P)<epsilon but there is one thing that...

hello all i just wanted to ask how would one prove that a function is riemann integrable through the definition that the lower integral has to equal the upper integral, an example on the function f(x)=x^2 would be of great help thanxs

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.

I have read what MathWorld has to offer on this and I am extremely confused. Could someone please explain this as simply as possible? Or then again maybe MathWorld already did that. Also, why is this function so important? Many thanks, Jameson

Hello guys, I am following the chapter about multiple Riemann integrals in Apostol's Mathematical Analysis. Theorem 14.11 says this (I translate from spanish to english): "Let S be a Jordan measurable set. Let the function f be defined and bounded in S. Then f is Riemann integrable if and...

How does the difference quotient undo what the Riemann sum does or vice versa. In terms of the two formulas? I would assume that working a difference quotient backwards would be similar to working a Riemann sum forward, but in reality as the operations go this couldn't be further from the...

I have been working on this problem for a while. I am supposed to prove that log 2 = \lim_{n \rightarrow \infty} \frac{1}{n+1} + \frac{1}{n+2} + ... + \frac{1}{2^n}. The problem is that I have a hard time figuring out how I am supposed to prove that something is equal to a transcendental...

so riemann integral pretty much says that if you take closer and closer approximations, then you can find the area of whatever(not too precise, I know, but doing the rectangles and stuff). I'm looking for a proof of it, but all I can find are more general things, i.e, Riemann integeral is...

Can anyone please direct me in the right way on working out the approximate area of a semi-circle with equation y = (r^2 - x^2)^0.5, by using a Riemann Sum

Could someone explain me what robustness is(in ur words), and how it works in proofs. All i kno is that basically u have two functions and u jiggle them a lot until u make them integrable if its not or destroy their integrability if they are integrable. Geometric explanation would really help...

Hey, when calculating the Riemann curvature tensor, you need to calculate the commutator of some vector field V , ie like this :- [\bigtriangledown_a, \bigtriangledown_b] = \bigtriangledown_a\bigtriangledown_b - \bigtriangledown_b\bigtriangledown_a = V;_a_b - V;_b_a But...

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...

So I'm supposed to describe the riemann surface of the following map: w=z-\sqrt{z^2-1} I can sort of understand the basic idea and derivation behind the riemann surfaces of w=e^z and w=\sqrt{z}, but ask me a question about another mapping, and I really don't know where to begin. How does one...

Ok, I am told in a complex analysis book that the gradient squared of u is equal to the gradient squared of v which is equal to 0. We know the derivate of w exists, and w(z)=u(x,y) + iv(x,y) Thus the Cauchy Riemann conditions must hold. (When I use d assume that it refers to a partial...

Please tell me if I am doing the summation of rectangular areas wrongly. Using summation of rectangles, find the area enclosed between the curve y = 3x^2 and the x-axis from x = 1 to x = 4. Now, before I answer the way it asks, I want to use antidifferentiation first to see what I should...

I'm looking for a proof of the Riemann mapping theorem. If I'm not mistaking, there are differnet proofs and the original proof is quite difficult. I'd appreciate any information on where I can/might find a less complicated proof of this theorem.

Does someone here knows something about how tensor of curvature (Riemann) and the hamilton operator associated with a particle are connected ? Makes this question sense ? Thanks

In trying to get my head round GR and quantum gravity, I'm puzzled about the following questions: Is the gauge group for gravity defined as the group of all possible Weyl tensors on a general 4D Riemann manifold? How is this group defined in matrix algebra? Is it a subgroup of GL(4). How do...

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?

Hi there, I have a problem and I was wondering if anyone can help me this one. Q)Suppose f:[a,b]->R is (Riemann) integrable and satisfies m<=f(x)<=M for all element x is a member of set [a,b]. Prove from the defintion of the Riemann integral that m(b-a)<=int[f(x).dx]<=M(b-a). where the...

Hello there, can anyone help me here as I'm finding it difficult to tackle this question. Consider f(x)=x^3 on the interval [1,5]. Find the Riemann sum for the equipartition P=(1,2,3,4,5) into 4 intervals with x_i^* being the right-hand endpoints (ie. x_i=a+hi) Then find a formula for the...

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