WebAnalytic Properties of Automorphic L-Functions is a three-chapter text that covers considerable research works on the automorphic L-functions attached by Langlands to reductive algebraic groups. Chapter I focuses on the analysis of Jacquet-Langlands methods and the Einstein series and Langlands’ so-called “Euler products . Web4. Automorphic L-functions for unitary groups 32 4.1. L-functions 32 4.2. Strategy for proving algebraicity of certain values of L-functions 34 4.3. The doubling method, in the setting of unitary groups 37 4.4. The doubling method, revisited from the perspective of algebraic geometry 44 4.5. Algebraicity of Eisenstein series 46 5.
Eisenstein Series and Automorphic Representations
WebLet τ be a complex number with strictly positive imaginary part.Define the holomorphic Eisenstein series G 2k (τ) of weight 2k, where k ≥ 2 is an integer, by the following series: = (,) {(,)} (+).This series absolutely converges to a holomorphic function of τ in the upper half-plane and its Fourier expansion given below shows that it extends to a holomorphic … Web10 Analysing Eisenstein Series and Small Representations 219 10.1 The SL (2, R) Eisenstein Series as a Function of s 220 10.2 Properties of Eisenstein Series 223 10.3 Evaluating Constant Term Formulas 232 10.4 Evaluating Spherical Whittaker Coec ients 242 11 Hecke Theory and Automorphic L-functions 255 11.1 Classical Hecke … owner operator jobs in new york
AMS :: Shahidi, Eisenstein Series and Automorphic L-Functions
WebThis introduction to automorphic forms on adelic groups G(A) emphasises the role of representation theory. The exposition is driven by examples, and collects and extends many results scattered throughout the literature, in … Web2. Eisenstein series and intertwining operators Let π be a cuspidal automorphic representation of M(A). We will always assume that the central character of π is trivial on A M and consider π as a subspace of L2(A MM(F)\M(A)). Let Aπ P denote the space of automorphic forms ϕ on U(A)M\G(A) such that for all k ∈ K the function m 7→ δ P(m ... WebContents Introduction 1 Chapter1. ReductiveGroups 7 §1.1.Preliminariesonreductivegroups 7 §1.2.Parabolicsubgroups 8 §1.3.Adelization 11 §1.4. L–groups 12 §1.5.ParabolicsubgroupsofL–groups 14 §1.6.Appendices 15 owner operator jobs in philadelphia