Dirichlet Characters: Definition and Properties

This lecture covers the definition and properties of Dirichlet characters, starting with a brief explanation of how they are defined and extending to their application to integers. The instructor guides the student through the concept of periodicity, boundedness, and the Dirichlet L-series function. The mock exam includes questions on proving properties related to Dirichlet characters, such as the sum of characters being bounded by a certain value and the equivalence between the prime number theorem and the Dirichlet L-series function. The student is asked to demonstrate their understanding through proofs and explanations, showcasing their knowledge of number theory and analytical functions.