A math course explaining the Riemann zeta function
Curated by: Zeta Explained (121 videos)
This is the 31st 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 introduces a few examples of Dirichlet series and some some basic theory of Dirichlet series. 00:00 - Intro and Examples of Dirichlet Series 02:50 - Definitions 04:00 - Zeta squared 09:55 - Multiplying two Dirichlet Series 12:42 - Dirichlet convolution formula 20:18 - Computing the Dirichlet series for ζ'(s) using convolution 27:37 - Table of series so far