Introduction to number theory lecture 48 Proof of the prime number theorem

This lecture is part of my Berkeley math 115 course “Introduction to number theory”
For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj53L8sMbzIhhXSAOpuZ1Fov8

We sketch the main ideas behind the proof of the prime number theorem.

Zagier’s paper with a short proof can be found at https://www.jstor.org/stable/2975232

The textbook is “An introduction to the theory of numbers” by Niven, Zuckerman, and Montgomery (5th edition).