Difference between revisions of "Dirichlet L-function"

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(Created page with "=References= [http://empslocal.ex.ac.uk/people/staff/mrwatkin//zeta/devlin.pdf How Euler discovered the zeta function]")
 
 
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Let $\chi$ be a [[Dirichlet character]]. The Dirichlet $L$-function associated with $\chi$ is
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$$L(s,\chi)=\displaystyle\sum_n \dfrac{\chi(n)}{n^s} = \displaystyle\prod_{p \hspace{2pt} \mathrm{prime}} \dfrac{1}{1-\chi(p)p^{-s}}.$$
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=References=
 
=References=
 
[http://empslocal.ex.ac.uk/people/staff/mrwatkin//zeta/devlin.pdf How Euler discovered the zeta function]
 
[http://empslocal.ex.ac.uk/people/staff/mrwatkin//zeta/devlin.pdf How Euler discovered the zeta function]
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[[Category:SpecialFunction]]

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