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Riemann Zeta Function and Riemann's Hypothesis - Introduction
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In this video, I have tried my best to introduce Riemann's #Zeta Function.
I have seen many people have a little problem and misconceptions on infinite sums like sum of all integers = -1/12. In this video, I have tried to understand those using #Analytic_Continuation.
A brief discussion of #Riemann_Hypothesis is also given. The zeroes of zeta functions are also discussed and an example is given on why #non-trivial zeroes of the zeta function are important.
Articles:
I hope you have enjoyed it and learned something new.
Happy Learning and forgive me for my troubling English.
0:09 Introduction
1:38 Zeta Definition
4:30 Complex Exponent
10:00 Proof of convergence
11:05 Zeta for complex inputs
13:10 Analytic Continuation
15:22 Zeta for full plane
16:48 Zeros of the zeta function
20:24 Riemann Hypothesis
22:05 Prime counting function
25:20 Non-trivial zeroes and Riemann prime counting function
_____________________________________________________________
Music used
Summit - by Jonny Easton
Check out his channel
______________________________________________________________
I have seen many people have a little problem and misconceptions on infinite sums like sum of all integers = -1/12. In this video, I have tried to understand those using #Analytic_Continuation.
A brief discussion of #Riemann_Hypothesis is also given. The zeroes of zeta functions are also discussed and an example is given on why #non-trivial zeroes of the zeta function are important.
Articles:
I hope you have enjoyed it and learned something new.
Happy Learning and forgive me for my troubling English.
0:09 Introduction
1:38 Zeta Definition
4:30 Complex Exponent
10:00 Proof of convergence
11:05 Zeta for complex inputs
13:10 Analytic Continuation
15:22 Zeta for full plane
16:48 Zeros of the zeta function
20:24 Riemann Hypothesis
22:05 Prime counting function
25:20 Non-trivial zeroes and Riemann prime counting function
_____________________________________________________________
Music used
Summit - by Jonny Easton
Check out his channel
______________________________________________________________
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