One of the best thing about this channel is knowing one of the greatest mathematicians also get confused with signs and some definition often not even trying to hide it. Best respect.
This really is the best math channel out there now. We are so lucky. (And Borcherds cannot but be pretty hilarious at times. Idkw, but accidental comic relief is so much more satisifying than all the people out there writing scripts.)
How do you reconcile the fact that for the integral over the small circle to vanish Re(s)>0 and later for the integral over the big arc to vanish Re(s)
This fascinated me years ago, when i was able to relate the Sine function in terms of reflections of Gamma and Zeta. Creepy almost... that in a way, prime numbers are a subtle hidden element in the Trig functions.
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One of the best thing about this channel is knowing one of the greatest mathematicians also get confused with signs and some definition often not even trying to hide it. Best respect.
This really is the best math channel out there now. We are so lucky.
(And Borcherds cannot but be pretty hilarious at times. Idkw, but accidental comic relief is so much more satisifying than all the people out there writing scripts.)
You have quickly risen to my favorite math channel. Top notch content bruh!!!
"If I don't tell you which way I'm going around the contour you can't catch my sign errors" lol
Thank you for your explanations of the contours. I got totally lost reading Edward's "Riemann's zeta function" for this exact reason.
I love how it's not at all explained rigorously, but still exact
How do you reconcile the fact that for the integral over the small circle to vanish Re(s)>0 and later for the integral over the big arc to vanish Re(s)
Profwssor, if I am not mistaking, this is not a Bromwich contour (which is used in inverse Laplace) but a Hankel contour.
At 6:55 should the fraction be equal to the geometric series 1 + e^(-z) + e^(-2z) + ... ? Did you forget the 1 or does it not matter
Since there's no 1 term, we have e^(-z)/(1-e^(-z)) which becomes the written 1/(e^z-1) when you multiply by 1 in the form e^z/e^z.
@@diribigal Ah, I see, thank you. I didn't see that negative sign.
This fascinated me years ago, when i was able to relate the Sine function in terms of reflections of Gamma and Zeta. Creepy almost... that in a way, prime numbers are a subtle hidden element in the Trig functions.
WE LOVE YOU RICHARDS
I feel confused, I keep getting sign errors or are there sign errors in the video?
Probably both
He did say preemptively that he gets the sign wrong 50% of the times 😂
Awesome
yeee