A math course explaining the Riemann zeta function
Curated by: Zeta Explained (121 videos)
This is the third 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 uniform convergence of the partial sums of zeta in the region Re(s) greater than 1, and shows that zeta is an analytic function in this region. 00:00 - Intro 01:24 - Intro to Uniform Convergence 02:34 - Difference between Pointwise Convergence and Uniform Convergence 08:41 - Proof that the partial sums of ζ(s) are uniformly convergent in the region "Re(s) is at least (1+a)" 16:08 - Complex analysis, why uniform convergence matters, analytic functions