2-Automorphic 2-groups

Automorphic forms on GL(2)

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 ofGL...

Nonvanishing of Gl ( 2 ) automorphic L functions at 1 / 2

Let k be a number field with ring of adeles A, let B be a quaternion algebra defined over k, and letG = B×. Let π be an infinite dimensional irreducible cuspidal automorphic representation of G(A). Then the vanishing or nonvanishing of L(1/2, π) has been conjectured or shown to be equivalent to conditions of considerable interest in number theory or automorphic representation theory. For exampl...

braiding from 2-groups to 2-groupoids

we give the concept of ‘braiding’ for 2-groupoids, and we show that this structure is equivalent tobraided regular, crossed modules.

Automorphic Representations of Adele Groups

2 00 9 Automorphic orbits in free groups : words versus subgroups ∗

We show that the following problems are decidable in a rank 2 free group F2: does a given finitely generated subgroupH contain primitive elements? and does H meet the orbit of a given word u under the action of G, the group of automorphisms of F2? Moreover, decidability subsists even if we restrict G to be a rational subset of the set of invertible substitutions (a.k.a. positive automorphisms)....