Functional equation (L-function): Difference between revisions

Revision as of 12:44, 4 October 2020

Revision as of 19:13, 7 October 2020

Line 20:

where ''Z''(''s'') is ζ(''s'') 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 on the embeddings of ''K'' (in algebraic terms, on the [[tensor product of fields|tensor product]] of ''K'' with the [[real number|real field]]).

There is a similar equation for the [[Dirichlet L-function]]s, but this time relating them in pairs:<Refref>{{cite web|url=https://dlmf.nist.gov/25.15 |title=§25.15 Dirichlet -functions on NIST}}</ref>

:<math>\Lambda(s,\chi)=\varepsilon\Lambda(1-s,\chi^*)</math>

Line 39:

*[[explicit formula (L-function)]]

*[[Riemann–Siegel formula]] (particular approximate functional equation)

==References==

{{Reflist}}

== External links ==