Prime Number Theorem

This lecture completes the proof of Von Mangoldt's explicit formula for the number of primes and uses it along with the classical zero free region for Zeta to prove the Prime Number Theorem. The instructor covers various mathematical concepts, including Peron's formula, arithmetic functions, absolutely convergent series, and pole analysis. The lecture delves into the behavior of Zeta functions, the distribution of prime numbers, and the order of poles. The proof involves detailed calculations and derivations, leading to a deep understanding of prime number distribution.