Dirichlet Series: Analytic and Algebraic Properties

This lecture covers the analytic and algebraic properties of Dirichlet series associated with arithmetic functions, including the abscissa of absolute and simple convergence, convolution of two arithmetic functions, and examples of Dirichlet series for various arithmetic functions. The instructor explains the convergence criteria, the behavior of partial sums, and the relationship between the properties of arithmetic functions and the Dirichlet series. The lecture also delves into the properties of the Riemann zeta function and the von Mangoldt function, providing examples and proofs to illustrate the concepts.