• DOI:10.1007/BFB0058988
• Corpus ID: 122773458

Automorphic Forms on GL(2)

@inproceedings{Langlands1970AutomorphicFO,
  title={Automorphic Forms on GL(2)},
  author={Robert P. Langlands},
  year={1970}
}

• R. Langlands
• Published 1970
• Mathematics

In [3] Jacquet and I investigated the standard theory of automorphic forms from the point of view of group representations. I would like on this occasion not only to indicate the results we obtained but also to justify our point of view. For us it is imperative not to consider functions on the upper half plane but rather to consider functions on GL(2,Q)\GL(2,A(Q)) where A(Q) is the adéle ring of Q. We also replace Q by an arbitrary number field or function field (in one variable over a finite field) F . One can introduce [3] a space of functions, called automorphic forms, and the notion that an irreducible representation π of GL(2,A(F )) is a constituent of the space of automorphic forms on GL(2, F )\GL(2,A(F )). Such a representation can in a certain sense be written as a tensor product