Dirichlet L-function
In mathematics, a Dirichlet L-series is a function of the form
Here χ is a Dirichlet character and s a complex variable with real part greater than 1. By analytic continuation, this function can be extended to a meromorphic function on the whole complex plane, and is then called a Dirichlet L-function and also denoted L(s, χ).
These functions are named after Johann Peter Gustav Lejeune Dirichlet who introduced them in (Dirichlet 1837) to prove the theorem on primes in arithmetic progressions that also bears his name. In the course of the proof, Dirichlet shows that L(s, χ) is non-zero at s = 1. Moreover, if χ is principal, then the corresponding Dirichlet L-function has a simple pole at s = 1.
Read more about Dirichlet L-function: Zeros of The Dirichlet L-functions, Euler Product, Functional Equation, Relation To The Hurwitz Zeta-function