Johann Peter Gustav Lejeune Dirichlet

1. Dirichlet Series

A generalization of the Zeta function.

$$ F(s) = \sum_{n=1}^\infty \frac{a_n}{n^s} $$

2. Class Number Formula

Relating algebraic number theory quantities to L-function values.

$$ h = \frac{w\sqrt{|D|}}{2\pi} L(1, \chi) $$