Zeta Explained Course

Currently Playing: Zeta Explained #47: The Truncated Explicit Formula for ψ(x)

This is the 47th 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 "The Riemann Zeta-Function: Theory and Applications" by Aleksandar Ivić. This particular video covers the proof of the truncated explicit formula for Chebyshev's ψ(x) function which counts up by log p on prime powers. 00:00 - Intro 08:10 - Two lemmas on integrals that give indicator functions 16:10 - Proof