Georg Friedrich Bernhard Riemann (German: [ˈɡeːɔʁk ˈfʁiːdʁɪç ˈbɛʁnhaʁt ˈʁiːman] (listen); 17 September 1826 – 20 July 1866) was a German mathematician who made contributions to analysis, number theory, and differential geometry.
In the field of real analysis, he is mostly known for the first rigorous formulation of the integral, the Riemann integral, and his work on Fourier series. His contributions to complex analysis include most notably the introduction of Riemann surfaces, breaking new ground in a natural, geometric treatment of complex analysis.
His famous 1859 paper on the prime-counting function, containing the original statement of the Riemann hypothesis, is regarded as one of the most influential papers in analytic number theory.
Through his pioneering contributions to differential geometry, Riemann laid the foundations of the mathematics of general relativity. He is considered by many to be one of the greatest mathematicians of all time.
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.
let be the product R(s)R(s+a) with a a complex or real number..the i would like to know the limit Lim(s tends to e) being e a number so R(e)=0 ¿is there a number a so the limit is non-zero nor infinite?..thanks.
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...
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...