Editing L-function (section)

== Rise of the general theory ==

This development preceded the [[Langlands program]] by a few years, and can be regarded as complementary to it: Langlands' work relates largely to [[Artin L-function|Artin ''L''-functions]], which, like [[Hecke L-function (disambiguation)|Hecke ''L''-functions]]<!-- intentional link to DAB page -->, were defined several decades earlier, and to ''L''-functions attached to general [[automorphic representation]]s.

Gradually it became clearer in what sense the construction of [[Hasse–Weil zeta function]]s might be made to work to provide valid ''L''-functions, in the analytic sense: there should be some input from analysis, which meant ''automorphic'' analysis. The general case now unifies at a conceptual level a number of different research programs.