A math course explaining the Riemann zeta function
Curated by: Zeta Explained (121 videos)
This is the fourth 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 (1) the Euler product formula, (2) a series expansion for zeta squared involving the divisor function, and (3) a proof of the generalized Euler product formula. 00:00 - Intro 00:56 - Usual proof 01:54 - Usual proof: Multiplying out the infinite product 04:29 - Multiplicative functions 06:14 - The "number of divisors" function 08:11 - ζ^2(s) 08:49 - Proof of ζ^2(s) 17:32 - Mention of "Dirichlet series" 18:02 - Generalized Euler Product Formula 19:37 - Proof of Generalized Euler Product Formula