Recent content by camilus

No, I'm willing to bet those things are by definition to make the mathematics work, the electron doesn't have physically infinite charge. Period.

Hi guys, I'm a mathematician from Miami Florida working in paraquaternionic and symplectic differential geometry, but I come from a very extensive physics background, pretty much well-versed in all modern physics. But my favorite of all is probably the philosophy of mathematics and science as...

Can anyone explain or point me to a good resource to understand these operators? I'm trying to the understand determinants for skew symmetric matrices, more specifically the Moore determinant and it's polarization of mixed determinants. Can hone shed some light? I'm confused as to how the...

For a map between vector bundles (which commute with a certain Lie groups like Sl2R or GL2R), what does it mean exactly for a fiber to be multiplicity free? Eplanations would be good, but examples would be even better. Thanks in advance, Gauss bless you! CM

Thanks a lot guys, I especially appreciate the different responses/viewpoints. I'm going to give them all a try and see which fits my mental conception of the manifold best. Thanks again! CM

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Let n <= m and G:=Gr(n,m) be the (real) Grassmanian manifold. I understand the topology of the simplest case, that of projective space, and am wondering if there is a way to interpret the topology of the G to similar to projective space, with the according generalizations needed. If V^n is an...

Show that n^2-n-1>n for n>2 and apply Bertrand's postulate that there is a prime in [n,2n] for all n>2.

What about the negative one?

Should \prod_\mathbb{P} \left( \sum_{\mathbb{Z} \ge 0} p^{-s n} \right) ^{-1} have that ^(-1) after it? Or am I missing something..? Are you rewriting 1/(1-p^-s) using geometric series? Anyways, thanks that was very helpful, I'm looking into the proofs of the product formula via this route.

I need help understanding this equality: \prod_{p-prime} \frac{1}{1+\frac{1}{p^3}}= \sum_{k=1}^\infty \frac{(-1)^{\sum_p ord_p(k)}}{k^3} Any help is greatly appreciated!

The step going from the second to last line, to the last line.

Hi everyone. I'm trying to understand the step where they wrote 1/2 ∏1/(1+p^-3) =1/2 Ʃ(-1)^ord(k)/k^3 How can I see this? I know the Euler product formula, but it has a negative sign before the p^-3, where here we have a + sign. Thanks for the help.

That it is a linear combination of z and (x-t), g=zg'+(x-t)g" for g',g" in k[x,y,z,t]. The question is what we do from there. We know that g(0,0,z,t)=0 (because g in I) hence g(0,0,z,t)=zg'(0,0,z,t)-tg"(0,0,z,t)=0. But from here can we conclude that g',g" are in I? I don't see how to do it..

I have already proved that (and thought of that), but the problem is that these are ideals of a polynomial ring, so that if I+J=k[x] then either I or J IS k[x], otherwise you could not generate the scalars in the field.. (since k-field, it has no nontrivial ideals) So this approach won't work...