The theory is particularly well developed for symmetric spaces and provides a theory of automorphic forms ( discussed below ).
42.
These examples are of interest and frequently applied in mathematical physics, and contemporary number theory, particularly automorphic representations.
43.
In the theory of Shimura varieties it associates automorphic representations of other groups to certain-adic Galois representations as well.
44.
In his 1884 book on the icosahedron, Klein set out a theory of automorphic functions, connecting algebra and geometry.
45.
The former case is said to be idiomorphic ( or " automorphic " ); the latter is xenomorphic.
46.
The Artin conjecture then follows immediately from the known fact that the L-functions of cuspidal automorphic representations are holomorphic.
47.
This is almost possible and leads to a description of all automorphic forms in terms of these constructs and cusp forms.
48.
A proof of Langlands functoriality would also lead towards a thorough understanding of the analytic properties of automorphic L-functions.
49.
There are three fundamental approaches to constructing measures of network similarity : structural equivalence, automorphic equivalence, and regular equivalence.
50.
There is a hierarchy of the three equivalence concepts : any set of structural equivalences are also automorphic and regular equivalences.
