anyone there?

yes

@JasperLoy keep making videos, never stop :D, keep singing

Hi @DanielFischer.

Hi

@quid Terence Tao thinks the Hilbert Polya Conjecture is false. Or at least he questions it here youtube.com/watch?v=nXNvaTFhX1c at 23:25

@DanielFischer I learnt the Jensen's formula yesterday.

Essentially a generalization of Newton's formula, right?

@BalarkaSen Jensen as in counting zeros of holomorphic functions? Which of Newton's formulae?

That is, the last coefficient of a polynomial is product of it's zeroes.

If the polynomial is monic (and we have a sign, $(-1)^{\deg p}$). Okay, and what has that to do with Jensen?

The version of Jensen I have in mind is $\log|f(0)| = \sum \log|z_k/r| + \frac1{2\pi} \int_0^{2\pi} \log|f(re^{i\theta})| d\theta$.

Where $z_k$ are the zeroes of $f$ inside a closed disk in the domain of holomorphicity of $f$.

If I let $f$ to be a polynomial, that tells me $|a_0| = |z_1 \cdots z_n|$ where $a_0$ is the last coefficient of the polynomial.

Is that a workable intuition for Jensen? How do you think about it? (I don't have a particular intuition for the term representing average of $\log|f(z)|$ over the circle of radius $r$)

Mmh, indeed, if you look at it that way, it is a generalisation of Newton's formula.

The average is the value of the solution of the Dircihlet problem at the centre. The solution of the Dirichlet problem is $\log \lvert f/B\rvert$, where $B$ is the (scaled for $r$) Blaschke product formed by the zeros of $f$.

@DanielFischer Um, I am not sure if I understand that. By Dirichlet problem, you mean that extending functions on circles to harmonic functions on disks, yes? How does this relate to this?

@JasperLoy: good to know. in a week, it's mine.

@BalarkaSen: how's it going?

@JasperLoy: I hope I become a great teacher in the future

@BalarkaSen For the boundary values $\log \lvert f\rvert$ on the disk $\lvert z\rvert < r$. $\log \lvert f\rvert$ is subharmonic on that disk (harmonic if $f$ has no zeros there).

@JasperLoy do you just sing or also play instruments ?

@JasperLoy: ever thought about practicing an instrument ?

ok, good luck with that

@DanielFischer Ah, I see.

@Huy So-so. What about you?

@BalarkaSen: good, drinking coffee. gonna prepare some stuff for my 9th graders later today.

and do some more planning for my 11th graders

mostly optimise my linear algebra stuff

nice

I threw out detailled discussion of rational functions from calculus

I hope that won't backfire

but I don't think I really use them anywhere else

I don't know many things to say about rational functions except the definition.

exactly

some teachers even told me they don't really discuss polynomial functions, but I think those I should keep

what do you discuss about polynomials? just curious.

just basics, how you can divide a root out, what the behaviour at roots is (according to multiplicity)

i see

I like to do it because otherwise getting eigenvalues in R^3 would be quite painful

(derivative also helps you figure out multiplicity of roots, by the way, but i suppose you'll discuss that)

yes, that I know

btw, do you know of any use of the characteristic polynomial except that its roots are eigenvalues?

no, not really.

do you think I should ask on main later today when more Americans are up

I've been wondering this yesterday

couldn't come up with anything useful

sure

I never remember: you did study linear algebra more or less already, right?

and analysis too, now?

Yes, I filled (and still filling) in the more fundamental things I didn't study.

good to know

But I am gathering rust on linear algebra because I am not really using it, although I know the theory.

Ted suggested doing some differential geometry might fix that.

I should revise basic physics

so I can come up with more examples

E.g., this didn't happen with point-set topology because I applied it frequently in the topology I learnt. Or the (multivariable) analysis/calculus I learnt because I am applying it in differential topology and the more advanced analysis I am learning right now.

@Huy basic physics is nice.

I always hated basic physics

I am learning some of that for my 11th grade studies

I thought more advanced physics would become more rigorous so I studied some of it

only to be even more disappointed

:P

@BalarkaSen: what book did you use to study linear algebra? Ted's?

No, Artin.

The first few chapters are all linear algebra and I think it's an excellent intro

@JasperLoy HAPPY BIRTHDAY, JASPER!!!

@JasperLoy :D

@JasperLoy What presents did you receive? If you can share.

@JasperLoy :D

@JasperLoy Don't worry much about it, I have similar experience. :-)

@JasperLoy I create my own gifts, my mathematical stuff which no one could ever give them to me. So, I'm happy.

bye

@JasperLoy Yeap, thanks.

@JasperLoy Sure. I'll let you know when my book is out.

@JasperLoy That's my destiny. :D

Is there a standard symbol for isotopy?

@Danu Not that I know.

Annoyingly, isotopy also means a lot of things.

Can base conversion be done in sublinear time?

@MatsGranvik thanks for this interesting information.

LOL math.stackexchange.com/questions/885907/…

Hi, I have a question about probability notation. If $F$ is a distribution, what does $\overline{F}(x)$ stand for? Is it $P(X>x)$?

Ramanujan: These steps you want, what you want, I do not know how to do.

Hardy: Well, you can just begin by trying your best and see if you don't surprise yourself.

as a mthematicians, playing a musical instrument is necessary to harmonise one person's passion/feeling/willing with his work and practise

yes necessary

as einstein played on both piano and was a good violinist

@LeakyNun i suppose yes

@Agawa001 Then how?

well, it is easier from hexa-quatrenary-octal-hexa

I'm talking about regular base conversions

not those special cases

(and those special cases are still linear time)

hi chat

@Semiclassical The master is back

riiight

there must be some tunnels from here and there, pay more time and see fantastic results

leeme check a blog i visited before

huh, that's weird. my icon is showing up next to these chat lines with a different color than in the room list

in the room list it's purple, but next to chat it's red.

and it's being inconsistent in a few other places, too

dunno i lost it sorry, some thing very impressive about linear jumping from bases

@Semiclassical Can base conversion be done in sublinear time?

no idea

one icon:

and the other:

@Semiclassical sure you have ideas

[i.stack.imgur.com/UR82V.png]

not really. i've never had an algorithms course

so stuff like sublinear time etc. are entirely outside my realm of expertise or interest

@Semiclassical i guess identicons change with user parameters, so make sure you log using same ones

weird.

@MatsGranvik You could rework the conjecture in such a way to accommodate that, though making it precise is probably just as hard: Namely, that the Riemann zeros are equivalent to a system in the same universality class as a Hermitean operator. (Rather than being directly equivalent to some Hermitian operator.)