Modularity theorem: Difference between revisions

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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 fieldsfield]]s are modular.{{sfn|Freitas|Le Hung|Siksek|2015}}

==Example==