But what is the Riemann zeta function? Visualizing analytic continuation
December 9, 2016
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22:11Now PlayingBut what is the Riemann zeta function? Visualizing analytic continuation
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as posted by the channelUnraveling the enigmatic function behind the Riemann hypothesis
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Music by Vince Rubinetti
Check out some of Vince's other work here
For those who want to learn more about complex exponentiation, here are a few resources:
My video on the topic
Mathologer's
Better Explained
For those who want to learn more about the relationship between 1+2+3+4+... and 1/12, I'm quite fond of this blog post by Terry Tao
Also, in a different video "What does it feel like to invent math", I give a completely different example of how adding up growing positive numbers can meaningfully give a negative number, so long as you loosen your understanding of what distance should mean for numbers
Interestingly, that vertical line where the convergent portion of the function appears to abruptly stop corresponds to numbers whose real part is Euler's constant, ~0.577. For those who know what this is, it's kind of fun to puzzle about why this is the case.
Thanks to these viewers for their contributions to translations
Hebrew: Omer Tuchfeld
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