2021-03-26

20:00

attachments/image_2021-03-26-20-00-58.png❗

  • What is a Dirichlet character?

    • A Dirichlet character is equivalent to a group homomorphism \begin{align*} \chi:(\mathbb{Z} / N)^{\times} \rightarrow \mathbb{C}^{\times} .\end{align*}

  • What is a Dirichlet L function?

    • Definition of a Dirichlet \(L{\hbox{-}}\)function:

\begin{align*} L(s ; \chi):=\sum_{n=1}^{\infty} \frac{\chi(n)}{n^{s}} =\prod_{p} \qty{ 1-\chi(p) p^{-s} }^{-1} .\end{align*}

#quick_notes