A math course explaining the Riemann zeta function
Curated by: Zeta Explained (121 videos)
This is the fifth 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 a proof that the zeta function has no zeros in the region Re(s) greater than 1. This is our first zero-free region. 00:00 - Intro and statement of the problem 00:44 - Start of proof 02:07 - The triangle inequality 04:38 - Resume proof 06:33 - The Taylor series of log(1+x) 07:08 - Resume proof 10:57 - Recap 11:23 - Next results