Difference between revisions of "Dirichlet L-function"

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Let $\chi$ be a [[Dirichlet character]] with [[conductor]] $f$. A Dirichlet $L$-function is
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Let $\chi$ be a [[Dirichlet character]]. The Dirichlet $L$-function associated with $\chi$ is
$$L(\chi,s)=\displaystyle\sum_n \dfrac{\chi(n)}{n^s} = \displaystyle\prod_{p \hspace{2pt} \mathrm{prime}} \dfrac{1}{1-\chi(p)p^{-s}}.$$
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$$L(s,\chi)=\displaystyle\sum_n \dfrac{\chi(n)}{n^s} = \displaystyle\prod_{p \hspace{2pt} \mathrm{prime}} \dfrac{1}{1-\chi(p)p^{-s}}.$$
  
 
=References=
 
=References=

Latest revision as of 19:27, 17 November 2016

Let $\chi$ be a Dirichlet character. The Dirichlet $L$-function associated with $\chi$ is $$L(s,\chi)=\displaystyle\sum_n \dfrac{\chi(n)}{n^s} = \displaystyle\prod_{p \hspace{2pt} \mathrm{prime}} \dfrac{1}{1-\chi(p)p^{-s}}.$$

References

How Euler discovered the zeta function