Functional equation (L-function): Difference between revisions

Revision as of 15:43, 21 August 2004

Revision as of 22:39, 1 November 2004

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There is a similar equation for the [[Dirichlet L-function]]s, but this time relating them in pairs:

:''&<math>\Lambda;''(''s'', &\chi;) = &epsilon;''&\varepsilon\Lambda;''(1 &minus; ''-s'', &\chi;^*)</math>

with &chi; a (primitive) [[Dirichlet character]], &chi;^* its complex conjugate, ''&Lambda;'' the L-function multiplied by a gamma-factor, and &epsilon; a complex number of [[absolute value]] 1, of shape

:''G''(&chi;)/|''G''(&chi;)|