A math course explaining the Riemann zeta function
Curated by: Zeta Explained (121 videos)
This is the 38th 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 the area of study known as the mean value theorems of the zeta function. 00:00 - Intro 03:32 - Theorem 1: mean value theorem for σ＞1 and proof 29:13 - Claim about 0＜σ＜1 and proof of Theorem 2 38:00 - Corollary 2: mean value theorem for 0＜σ＜1 40:19 - Theorem 3: mean value theorem for σ = 1/2