Mathematics

Forever Mozart

1:28 AM

@0celo7 that sounds good you should get it

0celo7

@ForeverMozart Already did.

It's better than $400 for a third edition lol

Forever Mozart

apparently someone found a flaw in the RH "proof"

0celo7

link?

Forever Mozart

math.stackexchange.com/questions/1896371/… see the comment at the very bottom of the page

he does not use ζ(s)ζ(s) has an Euler product anywhere, so his argument has to be flawed (because there are counter-examples with similar Ξ(t)Ξ(t) but having no Euler product and some zeros off the critical line)

maybe that is not a flaw though

maybe he just did not mention that $\zeta (s)$ has an Euler product anywhere

0celo7

I dunno

maybe it's right

Forever Mozart

1:36 AM

$\phi$

0celo7

a 4 page proof

he'll be the greatest mathematician of the century

If it seems to you that it should be trivial, why don't you try carrying out the proof? — Pedro Tamaroff ♦ 27 secs ago

@PedroTamaroff dam son

Forever Mozart

laying down the law

0celo7

he wrote that comment just as I finished writing a full answer

dunno if I should post it

trivial?

Forever Mozart

you could post it in one of those reveal boxes, and say he should at least try before revealing your solution

0celo7

how??

he's probably reading the same book I am

which is why I had an answer so quickly

> We claim that if a loop bounds a 2-chain, then the associated automorphism of $G$ is the identity

a 2-chain:

Forever Mozart

1:51 AM

2 many chains

0celo7

wtf is a bounding loop in a simplicial complex

0celo7

2:41 AM

@BalarkaSen I sat down to write a formal proof of the Poincare-intersection thing.

I showed that the Lefschetz number is $I(\Gamma,\Delta)$, which is wrong

It's $I(\Delta,\Gamma)$

crap

Hmm, this is weird

I'm not sure why the order of things matters in the proposition on page 121

0celo7

3:05 AM

Oh, no, I see

It's because of their definition of product orientation

yeah, this is strange

the Lefschetz theorem in Bredon is $[\Gamma]\cdot[\Delta]=L(f)$

but I seem to have proved that with a different sign.

Hmm.

@BalarkaSen THEOREM: Lefschetz number does not depend on the order in the intersection.

Proof. Let $n$ be the dimension of the compact manifold in question. If $n$ is odd, then $L(f)=I(\Delta,\Gamma)=(-1)^{n^2}I(\Gamma,\Delta)=0$.

If $n$ is even, then $L(f)=I(\Delta,\Gamma)=(-1)^{n^2}I(\Gamma,\Delta)=I(\Gamma,\Delta)$.

Lol

THERE GOES A WEEK OF MY LIFE

I've been stressing over that sign for a week.

user227867

3:33 AM

I wonder why people come to SE to learn math. I just learn it all by myself, or discuss with classmates or instructors.

user227867

Hi @robjohn is the fire over?

0celo7

no wait that's still wrong

it's not zero unless $f$ is homotopic to the identity...

hmm...

user227867

Looks like robjohn can't talk for now.

robjohn

@JasperLoy It is 85% contained

user227867

@robjohn I see. I now have 20 videos on my youtube channel. But I am thinking of redoing them all in HD, LOL.

Agawa001

9:48 AM

from now on one cant be able to torrent a book

user 1618033

10:41 AM

A new outstanding family of integrals developed here @robjohn

What a great day!

Let me find on youtobe some music about happiness because I'm soooooooo happpyyy today!!!

Pharrell Williams - Happy (Official Music Video)

►

(this part of research made my whole year, definitely)

0celo7

11:59 AM

@BalarkaSen There's an error in B-T.

Bredon and Gilkey can corroborate this statement.

> The existence of a Lefschetz formula holds more general in Weil cohomology theories (by definition) and hence notably in ℓ-adic étale cohomology.

wtf nLab

user1533609

12:15 PM

Anyone know about the associativity of permutations P and combination C operators

5P3P1 is (5P3)P1 OR 5P(3P1)

Agawa001

2:22 PM

just a bug maybe sorry

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$Mathematics$ Mathematics