Editing Modularity theorem (section)

==Generalizations==
The modularity theorem is a special case of more general conjectures due to [[Robert Langlands]]. The [[Langlands program]] seeks to attach an [[automorphic form]] or [[automorphic representation]] (a suitable generalization of a modular form) to more general objects of [[arithmetic algebraic geometry]], such as to every elliptic curve over a [[number field]].  Most cases of these extended conjectures have not yet been proved.

In 2013, Freitas, Le Hung, and Siksek proved that elliptic curves defined over real [[quadratic field]]s are modular.{{sfn|Freitas|Le Hung|Siksek|2015}}