Automorphic Forms, Representations and $L$-Functions
Title | Automorphic Forms, Representations and $L$-Functions PDF eBook |
Author | Armand Borel |
Publisher | American Mathematical Soc. |
Pages | 394 |
Release | 1979-06-30 |
Genre | Mathematics |
ISBN | 0821814370 |
Part 2 contains sections on Automorphic representations and $L$-functions, Arithmetical algebraic geometry and $L$-functions
Automorphic Forms and $L$-functions I
Title | Automorphic Forms and $L$-functions I PDF eBook |
Author | David Ginzburg |
Publisher | American Mathematical Soc. |
Pages | 315 |
Release | 2009 |
Genre | Mathematics |
ISBN | 0821847066 |
Includes articles that represent global aspects of automorphic forms. This book covers topics such as: the trace formula; functoriality; representations of reductive groups over local fields; the relative trace formula and periods of automorphic forms; Rankin - Selberg convolutions and L-functions; and, p-adic L-functions.
Automorphic Forms and L-functions for the Group GL(n, R)
Title | Automorphic Forms and L-functions for the Group GL(n, R) PDF eBook |
Author | D. Goldfeld |
Publisher | |
Pages | 493 |
Release | 2006 |
Genre | Automorphic forms |
ISBN | 9780511317057 |
L-functions associated to automorphic forms encode all classical number theoretic information. They are akin to elementary particles in physics. This book provides an entirely self-contained introduction to the theory of L-functions in a style accessible to graduate students with basic knowledge of classical analysis, complex variable theory, and algebra.
Analytic Properties of Automorphic L-Functions
Title | Analytic Properties of Automorphic L-Functions PDF eBook |
Author | Stephen Gelbart |
Publisher | Academic Press |
Pages | 142 |
Release | 2014-07-14 |
Genre | Mathematics |
ISBN | 1483261034 |
Analytic 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 . This chapter explains how local and global zeta-integrals are used to prove the analytic continuation and functional equations of the automorphic L-functions attached to GL(2). Chapter II deals with the developments and refinements of the zeta-inetgrals for GL(n). Chapter III describes the results for the L-functions L (s, ?, r), which are considered in the constant terms of Einstein series for some quasisplit reductive group. This book will be of value to undergraduate and graduate mathematics students.
Automorphic Forms and $L$-functions II
Title | Automorphic Forms and $L$-functions II PDF eBook |
Author | David Ginzburg |
Publisher | American Mathematical Soc. |
Pages | 339 |
Release | 2009 |
Genre | Mathematics |
ISBN | 0821847082 |
Includes articles that represent global aspects of automorphic forms. This book covers topics such as: the trace formula; functoriality; representations of reductive groups over local fields; the relative trace formula and periods of automorphic forms; Rankin - Selberg convolutions and L-functions; and, p-adic L-functions.
Six Short Chapters on Automorphic Forms and L-functions
Title | Six Short Chapters on Automorphic Forms and L-functions PDF eBook |
Author | Ze-Li Dou |
Publisher | Springer Science & Business Media |
Pages | 131 |
Release | 2012-12-15 |
Genre | Mathematics |
ISBN | 3642287085 |
"Six Short Chapters on Automorphic Forms and L-functions" treats the period conjectures of Shimura and the moment conjecture. These conjectures are of central importance in contemporary number theory, but have hitherto remained little discussed in expository form. The book is divided into six short and relatively independent chapters, each with its own theme, and presents a motivated and lively account of the main topics, providing professionals an overall view of the conjectures and providing researchers intending to specialize in the area a guide to the relevant literature. Ze-Li Dou and Qiao Zhang are both associate professors of Mathematics at Texas Christian University, USA.
Automorphic Forms and L-Functions for the Group GL(n,R)
Title | Automorphic Forms and L-Functions for the Group GL(n,R) PDF eBook |
Author | Dorian Goldfeld |
Publisher | Cambridge University Press |
Pages | 65 |
Release | 2006-08-03 |
Genre | Mathematics |
ISBN | 1139456202 |
L-functions associated to automorphic forms encode all classical number theoretic information. They are akin to elementary particles in physics. This book provides an entirely self-contained introduction to the theory of L-functions in a style accessible to graduate students with a basic knowledge of classical analysis, complex variable theory, and algebra. Also within the volume are many new results not yet found in the literature. The exposition provides complete detailed proofs of results in an easy-to-read format using many examples and without the need to know and remember many complex definitions. The main themes of the book are first worked out for GL(2,R) and GL(3,R), and then for the general case of GL(n,R). In an appendix to the book, a set of Mathematica functions is presented, designed to allow the reader to explore the theory from a computational point of view.