Lectures related to Perron's formula

Establishes the classical zero free region for the Zeta function and starts the proof of the explicit formula for

\psi(x)

.

Covers the proof of the explicit formula for the non-vanishing of the zeta function at the 1-line.

Covers the proof of Von Mangoldt's formula and the Prime Number Theorem using Zeta functions and pole analysis.

Explores Mertens' theorems on prime estimates and the behavior of the Mobius function in relation to the prime number theorem.