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 |
| − | $$L(\chi | + | $$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}}.$$ |
=References= | =References= | ||
[http://empslocal.ex.ac.uk/people/staff/mrwatkin//zeta/devlin.pdf How Euler discovered the zeta function] | [http://empslocal.ex.ac.uk/people/staff/mrwatkin//zeta/devlin.pdf How Euler discovered the zeta function] | ||
| + | |||
| + | [[Category:SpecialFunction]] | ||
Latest revision as of 19:27, 17 November 2016
Let $\chi$ be a Dirichlet character. The Dirichlet $L$-function associated with $\chi$ is $$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}}.$$
