SupposeP is a parabolic subgroup ofGwith Levi factor M and σ = ⊗σv a cuspidal representation of M(A). Then Ind σ = ⊗vInd σv is a representation of G(A) which may not be irreducible, and may not even have a finite composition series. As usual an irreducible subquotient of this representation is said to be a constituent of it. For almost all v, Ind σv has exactly one constituent π◦ v containing t...

The purpose of this note is to describe a method for computing general automorphic forms. I have carried out only limited computational tests so far, and have not discovered any new automorphic forms using it. However, the method does identify some lifted cusp forms on GL(3) and until recently was the only general method to compute an automorphic form on a higher rank group. It generalizes the ...

Suppose P is a parabolic subgroup of G with Levi factor M and σ = ⊗σv a cuspidal representation ofM(A). Then Ind σ = ⊗vInd σv is a representation of G(A) which may not be irreducible, and may not even have a finite composition series. As usual an irreducible subquotient of this representation is said to be a constituent of it. For almost all v, Ind σv has exactly one constituent π ◦ v containin...

Two of the primary methods of constructing automorphic forms are the Langlands program and Howe's theory of dual pairs. The Langlands program concerns a reductive linear group G deened over a number eld. Associated to G is its dual group L G. The con-jectural principle of functoriality says that a homomorphism L H ! L G should provide a \transfer" of automorphic representations from H to those ...

In this paper, we study modular forms on two simply connected groups of type D4 over Q. One group, Gs, is a globally split group of type D4, viewed as the group of isotopies of the split rational octonions. The other, Gc, is the isotopy group of the rational (non-split) octonions. We study automorphic forms on Gs in analogy to the work of Gross, Gan, and Savin on G2; namely we study automorphic...

We prove a natural analogue of the Sato-Tate conjecture for modular forms of weight 2 or 3 whose associated automorphic representations are a twist of the Steinberg representation at some finite place. 2000 Mathematics Subject Classification: 11F33.

We prove a natural analogue of the Sato-Tate conjecture for modular forms of weight 2 or 3 whose associated automorphic representations are a twist of the Steinberg representation at some finite place.

In this paper, we study modular forms on two simply connected groups of type D4 over Q. One group, Gs, is a globally split group of type D4, viewed as the group of isotopies of the split rational octonions. The other, Gc, is the isotopy group of the rational (non-split) octonions. We study automorphic forms on Gs in analogy to the work of Gross, Gan, and Savin on G2; namely we study automorphic...

A lifting map from cuspidal automorphic representations of the Jacobi group G J to cuspidal auto-morphic representations of the group PGL(2) is constructed. The lifting also has a local deenition, and the local and global versions are compatible. The local lifts can be described in terms of equivalence classes of local representations. The main idea in the construction is to exploit the close r...

Let A be the ring of adeles a number field F. Given self-dual irreducible, automorphic, cuspidal representation ? GLn(A), with trivial central character, we construct its full inverse image under weak Langlands functorial lift from appropriate split classical group G. We do this by new automorphic descent method, namely double descent. This method is derived recent generalized doubling integral...