A math course explaining the Riemann zeta function
Curated by: Zeta Explained (121 videos)
This is the 44th 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. We follow the book "Riemann's Zeta Function" by H.M. Edwards. This particular video covers the wave interpretation of Riemann's explicit formulas for the prime counting functions π(x) and J(x) (using modern notation), where the frequencies of the waves are the imaginary parts of the nontrivial zeros of the zeta function, and the waves spike at the logs of prime powers. 00:00 - Zeros of the zeta function 03:44 - Math 11:20 - Walking through visualizations to go from raw cosine waves to prime counting functions. 15:16 - Visualization of Möbius inversion 22:56 - Turning J(x) into π(x)