Dedekind Function: Analytic Continuation and Euler Product Formula

This lecture covers the Dedekind function, its properties, and the proof for the series convergence. It also discusses the Euler product formula, the meromorphic continuation of the Dedekind function, and the Mertens theorem. The instructor explains the Dirichlet type theorem, the counting of prime ideals in number fields, and the analytic continuation of logarithmic functions. The lecture concludes with the proof of the theorems using specific results and the non-vanishing property of certain functions.