Here is an interesting article.
Math Gateway
And another:
Math Gateway
Here is an interesting article.
Math Gateway
And another:
Math Gateway
It is a thing in number theory.
A Dirichlet charachter is a function $\displaystyle \chi : \mathbb{F}_p^{\times}\mapsto \mathbb{C}^{\times}$ (here $\displaystyle \mathbb{F}_p^{\times}$ is the non-zero elements mod $\displaystyle p$ and $\displaystyle \mathbb{C}^{\times}$ are the non-zero complex numbers) which satisfies $\displaystyle \chi (ab) = \chi (a)\chi (b)$.
Given a Dirichlet charachter $\displaystyle \chi$ we form the Dirichlet L-series $\displaystyle L(\chi , s)= \sum_{n=1}^{\infty}\frac{\chi (n)}{n^s}$ where $\displaystyle s$ is complex.
It can be proven that $\displaystyle L(\chi , s)$ converges when $\displaystyle \Re (s) > 1$.
Using analytic continuation we extend this to a meromorphic function on $\displaystyle \mathbb{C}$.
This continued new function is called the Dirichlet L-function.
It is related to Riemann zeta function.