Sejad Ali Kais: From the Riemann Zeta L-function to the Artin L-function

Abstract: The thesis starts by talking about the Riemann Zeta function and then goes to develop the necessary algebraic number theory and representation tools to define and motivate the Artin L-function. The Artin L-function generalizes the Riemann Zeta function and the Dirichlet, Dedekind, and Hecke L-functions. We further prove that the Artin L-function admits a meromorphic continuation. The thesis focuses more on building the foundation to motivate the necessary machinery to define the Artin L-function and prove its meromorphic continuation, starting from the integers, expanding proofs and giving examples