The theory of Eisenstein series is fundamental for the spectral theory of automorphic forms. It was first developed by Selberg, and was completed by Langlands ([Lan76]; see also [MW95]). There are several known proofs for the meromorphic continuation of Eisenstein series (apart from very special cases of Eisenstein series which can be expressed in terms of Tate integrals). In all these proofs i...

In this thesis we study operators, and spaces of operators on a Hubert space defined by intertwining relations. The classical Hankel operators are those operators which intertwine the unilateral shift and its adjoint. We consider generalised Hankel operators relative to shifts and relative to families of shifts and give generalisations of the classical theorems of Nehari and Hartman. In contras...

Let G = GL(n, F ) where F is a local field of arbitrary characteristic, and let π1, π2 be representations induced from characters of two maximal parabolic subgroups P1, P2. We explicitly determine the space HomG (π1, π2) of intertwining operators and prove that it has dimension ≤ 1 in all cases.

The Z/2Z–graded intertwining operators are introduced. We study these operators in the case of “degenerate” N = 1 minimal models, with the central charge c = 3 2 . The corresponding fusion ring is isomorphic to the Grothendieck ring for the Lie superalgebra osp(1|2). We also discus multiplicity–2 fusion rules and logarithmic intertwiners.

We consider integrals of cuspforms f on reductive groups G defined over numberfields k against restrictions ι∗E of Eisenstein series E on “larger” reductive groups G̃ over k via imbeddings ι : G → G̃. We give hypotheses sufficient to assure that such global integrals have Euler products. At good primes, the local factors are shown to be rational functions in the corresponding parameters q−s from ...

1.1 Notation In this note, N denotes the set of non-negative integers, i.e. N = {0, 1, 2, . . . }. Let V be a C-linear space and z a formal variable. We introduce the following linear spaces: V [z] := {n∈N vnz | vn ∈ V, vn = 0 for all but finitely many n}, V [z, z−1] := {n∈Z vnz | vn ∈ V, vn = 0 for all but finitely many n}, V [[z]] := {n∈N vnz | vn ∈ V }, V [[z, z−1]] := {n∈Z vnz | vn ∈ V }, V...