Unlocking the Mystery of the Riemann Zeta Function & Hypothesis 🔍

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.

The article of Jorgen Veisdal can be found here: https://medium.com/cantors-paradise/the-riemann-hypothesis-explained-fa01c1f75d3f

Articles:
1. https://www.dropbox.com/s/iychwnb6qge1aze/thesis13.pdf?dl=0
2. https://www.semanticscholar.org/paper/The-Analytic-Expression-for-Riemann's-Prime-via-the-Milioto/009d51108c9f59b9a7226a98129dd9d8315b63cb
3. https://www.springer.com/gp/book/9783319914817
4. https://scholar.google.com/scholar?start=10&q=related:iWX4BRvXTv0lSM:scholar.google.com/&hl=en&as_sdt=0,5#d=gs_qabs&u=%23p%3DMt3PXWLGjQAJ
5. https://www.maths.tcd.ie/pub/HistMath/People/Riemann/Zeta/EZeta.pdf
6. https://www.amazon.in/Riemanns-Function-Dover-Books-Mathematics/dp/0486417409/ref=mp_s_a_1_1?dchild=1&keywords=riemann+zeta+function+book&qid=1603367168&sprefix=Riemann+zeta+&sr=8-1
7. https://www.amazon.in/Prime-Obsession-Berhhard-Greatest-Mathematics/dp/0452285259/ref=mp_s_a_1_1?dchild=1&keywords=prime+obsession&qid=1603367192&sr=8-1

I hope you have enjoyed it and learned something new.
Happy Learning and forgive me for my troubling English.

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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
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Music used
Summit - by Jonny Easton
Link: https://youtu.be/ZH5B_C8r9Dk
Check out his channel
Link: https://www.youtube.com/jonnyeaston
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