Difference between revisions of "Dirichlet L-function"
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| − | Let $\chi$ be a [[Dirichlet character]] | + | Let $\chi$ be a [[Dirichlet character]]. The Dirichlet $L$-function associated with $\chi$ is |
$$L(\chi,s)=\displaystyle\sum_n \dfrac{\chi(n)}{n^s} = \displaystyle\prod_{p \hspace{2pt} \mathrm{prime}} \dfrac{1}{1-\chi(p)p^{-s}}.$$ | $$L(\chi,s)=\displaystyle\sum_n \dfrac{\chi(n)}{n^s} = \displaystyle\prod_{p \hspace{2pt} \mathrm{prime}} \dfrac{1}{1-\chi(p)p^{-s}}.$$ | ||
Revision as of 19:27, 17 November 2016
Let $\chi$ be a Dirichlet character. The Dirichlet $L$-function associated with $\chi$ is $$L(\chi,s)=\displaystyle\sum_n \dfrac{\chi(n)}{n^s} = \displaystyle\prod_{p \hspace{2pt} \mathrm{prime}} \dfrac{1}{1-\chi(p)p^{-s}}.$$
