Riemann Zeta Function and Riemann's Hypothesis - Introduction

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. Visit cheenta.com for more. 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 Link: https://youtu.be/ZH5B_C8r9Dk Check out his channel Link: https://www.youtube.com/jonnyeaston ______________________________________________________________