Lectures related to Mertens function

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

Covers the Dedekind function, Euler product formula, series convergence, and analytic continuation of logarithmic functions.

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

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

\psi(x)

.

Explores the Euler product theorem and Perron's formula in number theory and complex analysis.

Introduces the Euler product and Perron's formula in arithmetic functions.