A math course explaining the Riemann zeta function
Curated by: Zeta Explained (121 videos)
This is the seventh video in a series explaining the Riemann zeta function. The idea of the series is to start with basics and eventually work our way to advanced topics. The viewer is expected to understand calculus and complex numbers, whereas I will try to explain concepts from complex analysis as needed. We will follow the book "The Riemann Zeta Function: Theory and Applications" by Aleksandar Ivić. This particular video covers analytic continuation, which will allow us to analyze the zeta function when the real part is less than 1. 00:00 - Intro 00:51 - Analytic Continuation 01:56 - The geometric series 04:35 - Computing a Taylor series 06:01 - Larger disc of convergence 07:46 - Graphical illustration 09:41 - The geometric series at z=2 12:59 - Analytic continuation for the zeta function series