Functional equation (L-function): Difference between revisions

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In [[mathematics]], the [[L-function]]s of [[number theory]] are expected to have several characteristic properties, one of which is that they satisfy certain '''[[functional equation]]s'''. There is an elaborate theory of what these equations should be, much of which is still conjectural. For example, the [[Riemann zeta function]] has a functional equation relating its value at the [[complex number]] ''s'' with its value at 1 − ''s''. In every case this relates to some value ζ(''s'') that is only defined by [[analytic continuation]] from the [[infinite series]] definition. That is, writing{{Ndashspaced ndash}}as is conventional{{Ndashspaced ndash}}σ for the real part of ''s'', the functional equation relates the cases

:σ > 1 and σ < 0,