Dirichlet L-functions and applications to Dirichlet's Theorem on prime

In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about the integers. It is often said to have begun with Peter Gustav Lejeune Dirichlet's 1837 introduction of Dirichlet L-functions to give the first proof of Dirichlet's theorem on arithmetic progressions. It is well known for its results on prime numbers. In this book, we define the Dirichlet L-function and its properties which is a special case of Dirichlet series, and give applications of this function in the analytic number theory in order to prove Dirichlet's Theorem on primes in arithmetic progressions.