A math course explaining the Riemann zeta function
Curated by: Zeta Explained (121 videos)
This is the 32nd 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 discusses the Möbius function μ(n), the Dirichlet series for 1/ζ(s), Möbius inversion, a generalized Möbius inversion formula, and applying Möbius inversion to the Chebyshev psi and theta functions. 00:00 - The Möbius function μ(n) 03:34 - The reciprocal of the Riemann zeta function 09:15 - Interpretation of ζ(s) * 1/ζ(s) = 1 16:43 - The Möbius Inversion Formula 19:48 - Second Möbius Inversion Formula 25:36 - Application to Chebyshev functions 35:57 - Teaser for next video