Functional equation (L-function): Difference between revisions

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The functional equation in question for the Riemann zeta function takes the simple form
 
:''<math>Z''(''s'') = ''Z''(1 &minus; ''-s'')</math>
 
where ''Z''(''s'') is multiplied by a ''gamma-factor'', involving the [[gamma function]]. This is now read as an 'extra' factor in the [[Euler product]] for the zeta-function, corresponding to the [[infinite prime]]. Just the same shape of functional equation holds for the [[Dedekind zeta function]] of a [[number field]] ''K'', with an appropriate gamma-factor that depends only the embeddings of ''K'' (in algebraic terms, on the [[tensor product of fields|tensor product]] of ''K'' with the [[real field]]).