i serisouly hate this type of questions: prove lim_{x -> a} f(x) = f(a) for a continnous function f

what do these people think they are teaching?

epsilon-delta techniques, obviously. these students are being asked to establish that functions are continuous at points instead of being told or allowed to take such for granted

@anon what are p-adic integrals for?

you can derive the functional equation of twisted L functions attached to number fields using adelic analysis. it's the same idea (poisson summation), but since it occurs over all places instead of just with the complex plane it is very appealing to a number theorist. there is also some application in pro-p zeta functions (which can be written as zeta integrals).

apparently it's also been used in some p-adic ergodic results for linear recurrence relation solutions

(which intuitively I suspect may be viewed as high-powered version of probabilistic congruence information... ish)

thanks. what's a twisted L function?

like a dirichlet l function, but you move up to number fields that aren't necessarily Q and define a hecke character on the ideals.

ok

oh that's cool

does it have applications to number theory?

maybe there's a prime ideal thoerem

it is number theory...

I mean concrete stuff, does it give new information about algebraic integers?

so I hear

@JacobBlack, categories for working mathematician, birkhoff & maclane, algebra chapter 0, artin galois theory

I only have the first two

????

no I didn't know that.. I meant maclane & birkhoff

@anon, I think you must see very deeply if you can appreciate something like that in the pure

hi @JacobBlack

nah

I only care about zeta functions because it tells about primes

for example

that's just my ignorance though

zeta functions are to number systems and algebraic structures what generating functions are to combinatorial families; they encode information. much like how various elements of the system/structure decomposes into parts, there is often local-global at play in euler product factorizations. in particular the twisted l functions are "musical" since they invoke fourier-analytic-type objects (characters)

@JacobBlack do you know: Siegel - topics in complex analysis? I want it

I get the use of zeta functions with dirichlet convolution for the study of multiplicative aspects & generating functions for the study of additive things (like partitions)

yeah maybe Siegel is like too much of a pick & mix to be really valuable at my beginner level

heya

Double derivatives all the way

Lets say i have a parametrication in $\mathbb{R}^2$, like $c(t) = \langle x(t), y(t) \rangle$. And my function is on the form $f(x,y) = \ldots$

Now I need to calculate $\cfrac{\mathrm{d}^2 h}{\mathrm{d} t^2}$ where $h = f \circ c$

I tried this

I am a tad unsure what $$\frac{\mathrm{d}}{\mathrm{d}t} \left( \frac{\mathrm{d}f}{\mathrm{d}x} \right)$$ equals..

Hmm this is all wrong

it tells you what it equals in the last line of the image, no? (and it uses the same rule you used to find dh/dt...)

Not sure why it's ignored. But isn't $C_d\le D_{2n}$ something we know a priori..?

what do you mean by a prior? I thought I proved it

oh

well it's obvious but I gave a reason why its true anyway

every subgroup of a group is ... a subgroup.

lol

what you want to show is that for every $i$, $\langle r^i\rangle\le\langle r\rangle\cong C_n$, and in cyclic groups, subgroups of a given order are unique

ah, that's a good point

thus any cyclic group of order greater than 2 must be a subgroup of that single copy of Cn, and in that single copy of Cd each cyclic subgroup is unique, which proves uniqueness overall

note that $\langle r^i\rangle\le\langle r\rangle$ follows from $r^i\in\langle r\rangle$; no divisibility argument is needed

and you'll want to distinguish $\langle \rm blah\rangle$'s from C_n. The latter is something like an isomorphism class, while in general distinct subgroups can be isomorphic. this is especially relevant when you're trying to show that each subgroup of D2n of a given isomorphism type is indeed unique.

I really hate not havingenough time to do the work I want to do

Me too

Can I have some help with my question Representation of the dual of Cb(X)?