Complex analysis: Weierstrass elliptic functions

This lecture is part of an online undergraduate course on complex analysis.

We define the Weierstrass P and zeta functions and show they are elliptic.

[xiaokangzhang]

Thank you Professor, these lectures are real gems

[daneka]

Good sense of humor combined with deep knowledge is a blessing

[faisalal-faisal]

"The other good thing about saying something is 'locally uniformally convergent' is that no one can quite remember the definition of it, so they'll probably give you a pass for whatever you want to claim for it" :)

[SG-kjuy]

Watching your interview video, I became a big fan of you.

[reinerwilhelms-tricarico]

Just looked it up: In LaTeX the Weierstrass P is \wp ($\wp$ in math mode).

[peisun]

Does anyone know any good lectures on Riemann geometry like this? I love watching lectures like these.

[narutosaga]

Wow that bit about the Tripos example questions, so darn glad that those kinds of questions are out of style now! Yikes

[.saar.a]

I wonder if it is preferable to introduce P' by the series and then Weierstrass P and Zeta as antiderivatives of P' and P respectively, via path integrals.
This works since P' and P do not have poles with nonzero residue. On the other hand however, it does not seem to have any technical advantages either other than that we do not have to tweak the convergence, which is not a big deal anyway....

[larspos]

The Riemann zeta function is locally uniformally convergent, therefore all it's non trivial zero's have real part 1/2

[zubin]

at 8:32 I was feeling guilty about not knowing the conditions for this property, then felt a lot better about my ignorance within the following 30 seconds :)

[JesusHernandez-xvlf]

Can anyone explain me more why the series in 2:42 does not converge absolutely?

[digosen]

This is possibly a very dumb question and has a simple solution, but is there any reason why the number of poles has to be an integer? Couldn't there be some function that effectively behaves as having a noninteger pole? (whatever that would mean). If so couldn't we use that to get an elliptic function of the same order?

[Vidrinskas]

Congrats to the senior wrangler in 1912. You earned it. 🤣