On standard L-functions attached to automorphic forms on definite orthogonal groups

On Zeta Functions of Orthogonal Groups of Single-class Positive Definite Quadratic Forms

Representations of Hecke–Shimura rings of integral single-class positive definite quadratic forms on relevant spaces of harmonic forms are considered, and the problem of simultaneous diagonalization of the corresponding Hecke operators is investigated. Explicit relations are deduced between zeta functions of the single-class quadratic forms in two and four variables corresponding to the harmoni...

Explicit Calculations of Automorphic Forms for Definite Unitary Groups

I give an algorithm for computing the full space of automorphic forms for definite unitary groups over Q, and apply this to calculate the automorphic forms of level G(Ẑ) and various small weights for an example of a rank 3 unitary group. This leads to some examples of various types of endoscopic lifting from automorphic forms for U1 × U1 × U1 and U1 × U2, and to an example of a non-endoscopic f...

Lectures on automorphic L-functions

PREFACE This article follows the format of five lectures that we gave on automorphic Lfunctions. The lectures were intended to be a brief introduction for number theorists to some of the main ideas in the subject. Three of the lectures concerned the general properties of automorphic L-functions, with particular reference to questions of spectral decomposition. We have grouped these together as ...

Lifting Automorphic Representations on the Double Covers of Orthogonal Groups

Suppose that G and H are connected reductive groups over a number field F and that an L-homomorphism ρ : LG −→ LH is given. The Langlands functoriality conjecture predicts the existence of a map from the automorphic representations of G(A) to those of H(A). If the adelic points of the algebraic groups G, H are replaced by their metaplectic covers, one may hope to specify an analogue of the Lgro...

Discontinuous Groups and Automorphic Forms