Mertens' Theorems and Mobius Function

This lecture discusses Mertens' theorems on prime estimates and how the prime number theorem implies the behavior of the Mobius function. The slides cover topics such as the partial sum of the Mobius function, logarithmic functions, and the application of Abel summation formula. The instructor explores the relationship between the prime number theorem and the Mobius function, providing insights into the order of the Mobius function up to x. The lecture delves into the analytical properties of Dirichlet series and their connection to arithmetic functions.