Learning

The Riemann Zeta Function: Analytic Continuation and Functional Equation

Complex Analysis Foundations → Generalizations and Dirichlet L-functions

This graduate-level path provides a rigorous, analytic-number-theoretic introduction to the Riemann zeta function. It begins with the necessary complex analysis and analytic number theory prerequisites, then develops the zeta function's initial definition, its analytic continuation to the complex plane, and its functional equation. The path culminates in an exploration of the zeros and the prime number theorem, with a brief look at generalizations.