Difference between revisions of "Dirichlet L-function"
From specialfunctionswiki
(Created page with "=References= [http://empslocal.ex.ac.uk/people/staff/mrwatkin//zeta/devlin.pdf How Euler discovered the zeta function]") |
|||
| Line 1: | Line 1: | ||
| + | Let $\chi$ be a [[Dirichlet character]] with [[conductor]] $f$. A Dirichlet $L$-function is | ||
| + | $$L(\chi,s)=\displaystyle\sum_n \dfrac{\chi(n)}{n^s} = \displaystyle\prod_{p \hspace{2pt} \mathrm{prime}} \dfrac{1}{1-\chi(p)p^{-s}}.$$ | ||
| + | |||
=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] | ||
Revision as of 04:08, 12 April 2015
Let $\chi$ be a Dirichlet character with conductor $f$. A Dirichlet $L$-function is $$L(\chi,s)=\displaystyle\sum_n \dfrac{\chi(n)}{n^s} = \displaystyle\prod_{p \hspace{2pt} \mathrm{prime}} \dfrac{1}{1-\chi(p)p^{-s}}.$$
