A Polya-Hilbert operator for automorphic L-functions

A Polya-hilbert Operator for Automorphic L-functions

A Polya Operator for Automorphic L-functions

Let k be a number field and letM be a simple k-algebra with center k of rank n, i.e. dimk(M) = n 2. Fix a k-involution x 7→ xτ on M , i.e. (xy)τ = yτxτ as well as (xτ )τ = x and xτ = x when x ∈ k. We will assume that M and τ are defined over the ring of integers O of k. The standard example will be the algebra of n× n matrices Matn(k) and x τ = xt the transposed matrix. For any ringR over k let...

Hilbert operator for automorphic L - functions and a local trace formula

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 ...

New Bounds for Automorphic L-functions

This dissertation contributes to the analytic theory of automorphic L-functions. We prove an approximate functional equation for the central value of the L-series attached to an irreducible cuspidal automorphic representation π of GLm over a number field. The approximation involves a smooth truncation of the Dirichlet series L(s, π) and L(s, π̃) after about √ C terms, where C denotes the analyti...