Automorphic Representations and L-Functions for the General by Dorian Goldfeld, Joseph Hundley

  • admin
  • April 2, 2017
  • Number Theory
  • Comments Off on Automorphic Representations and L-Functions for the General by Dorian Goldfeld, Joseph Hundley

By Dorian Goldfeld, Joseph Hundley

This graduate-level textbook offers an easy exposition of the speculation of automorphic representations and L-functions for the overall linear workforce in an adelic environment. The authors hold definitions to a minimal and repeat them whilst reintroduced in order that the e-book is offered from any access element, and without past wisdom of illustration thought. in addition they contain concrete examples of either worldwide and native representations of GL(n), and current their linked L-functions. the speculation is constructed from first rules for GL(1), then rigorously prolonged to GL(2) with entire exact proofs of key theorems. numerous of the proofs are the following awarded for the 1st time, together with Jacquet's uncomplicated and chic evidence of the tensor product theorem. ultimately, the better rank state of affairs of GL(n) is given an in depth remedy. Containing a variety of routines, this ebook will encourage scholars and researchers to start operating during this fertile box of analysis.

Show description

Read Online or Download Automorphic Representations and L-Functions for the General Linear Group: Volume 1 PDF

Best number theory books

Problems and Theorems in Analysis: Theory of Functions. Zeros. Polynomials. Determinants. Number Theory. Geometry

From the reports: ". .. some time past, extra of the best mathematicians proposed and solved difficulties than at the present time, and there have been challenge departments in lots of journals. Pólya and Szego should have combed the entire huge challenge literature from approximately 1850 to 1925 for his or her fabric, and their choice of the simplest in research is a historical past of lasting worth.

Introduction to Algebraic and Abelian functions

Creation to Algebraic and Abelian capabilities is a self-contained presentation of a primary topic in algebraic geometry and quantity concept. For this revised version, the cloth on theta features has been elevated, and the instance of the Fermat curves is carried through the textual content. This quantity is aimed toward a second-year graduate direction, however it leads obviously to the learn of extra complicated books indexed within the bibliography.

Solutions Manual to Accompany An Introduction to Numerical Methods and Analysis

A recommendations guide to accompany An advent to Numerical equipment and research, moment Edition

An creation to Numerical equipment and research, moment version displays the newest developments within the box, comprises new fabric and revised routines, and provides a special emphasis on functions. the writer truly explains tips on how to either build and review approximations for accuracy and function, that are key talents in numerous fields. quite a lot of higher-level equipment and recommendations, together with new themes reminiscent of the roots of polynomials, spectral collocation, finite point rules, and Clenshaw-Curtis quadrature, are provided from an introductory viewpoint, and theSecond version additionally features:

Chapters and sections that commence with easy, hassle-free fabric by way of slow insurance of extra complex material
routines starting from easy hand computations to demanding derivations and minor proofs to programming exercises
common publicity and usage of MATLAB
An appendix that includes proofs of assorted theorems and different fabric

Additional info for Automorphic Representations and L-Functions for the General Linear Group: Volume 1

Example text

Let S = {∞, p1 , p2 , . . , p } denote the finite set of primes such that x p ∈ Z p and h p is the characteristic function of Z p for p ∈ S. If α ∈ Q, it follows that h p (x p + α) = 0 for p ∈ S unless α is an integer in Z p . Since h v is a locally Adeles over Q 24 constant compactly supported function for v ∈ S this implies that there exists a rational integer M so that h(x + α) = 0 unless α = Mn with n ∈ Z. Therefore (at least formally) n . h(x + α) = h x+ M α∈Q n∈Z Finally, for fixed x ∈ AQ we must have that h x + Mn has rapid decay in n as n → ±∞.

Remarks A fundamental domain is precisely a choice of one point from each orbit of G. If G\X is the quotient space with the quotient topology and π : X → G\X is the quotient map, then the fundamental domain is the image of a section σ : G\X → X . ) The construction of an explicit fundamental domain for the action of the additive group Q on the adele group AQ is equivalent to a generalization of the ancient Chinese remainder theorem. 2 (Chinese Remainder Theorem) Let p1 , p2 , . . pn be distinct primes.

Hint: It may be useful to know that an infinite product (1 + an ) converges if the series an converges absolutely. 9 Show that a smooth adelic function f : AQ → C is continuous (for the adelic topology). 1. Prove that e(αu) du = Q\AQ 1, if α = 0, 0, if α = 0. 10. 10). We will show there is a smooth periodic adelic function g : AQ → C such that g(x) = f (x) − f (0) , 1 − e(x/N ) (†) whenever this expression makes sense. 10 to assume that each finite factor of h is of the form h p = 1a+ pm Z p for some a ∈ Q p and some integer m (that depend on the prime p).

Download PDF sample

Rated 4.69 of 5 – based on 12 votes