Modularity theorem: Difference between revisions

Content deleted Content added
Line 66:
 
==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. However,

Freitas, Le Hung, &and Siksek{{sfn|Freitas|Le Hung|Siksek|2015}}<!--{harvtxt|Freitas|Le Hung|Siksek|2015}}--> proved that elliptic curves defined over real quadratic fields are modular.{{sfn|Freitas|Le Hung|Siksek|2015}}
 
==Example==