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Author : Armand Borel
Publisher : American Mathematical Soc.
Page : 394 pages
File Size : 18,94 MB
Release : 1979-06-30
Category : Mathematics
ISBN : 0821814370
Part 2 contains sections on Automorphic representations and $L$-functions, Arithmetical algebraic geometry and $L$-functions
Author : A. Borel
Publisher : American Mathematical Soc.
Page : 334 pages
File Size : 30,53 MB
Release : 1979
Category : Mathematics
ISBN : 0821814354
Contains sections on Reductive groups, representations, Automorphic forms and representations.
Author : D. Bump
Publisher : Springer
Page : 196 pages
File Size : 27,67 MB
Release : 2006-12-08
Category : Mathematics
ISBN : 3540390553
Author : H. Jacquet
Publisher : Springer
Page : 156 pages
File Size : 26,50 MB
Release : 2006-11-15
Category : Mathematics
ISBN : 3540376127
Author : Dorian Goldfeld
Publisher : Cambridge University Press
Page : 65 pages
File Size : 18,65 MB
Release : 2006-08-03
Category : 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.
Author : Dorian Goldfeld
Publisher : Cambridge University Press
Page : 571 pages
File Size : 27,37 MB
Release : 2011-04-21
Category : Mathematics
ISBN : 1139500139
This graduate-level textbook provides an elementary exposition of the theory of automorphic representations and L-functions for the general linear group in an adelic setting. Definitions are kept to a minimum and repeated when reintroduced so that the book is accessible from any entry point, and with no prior knowledge of representation theory. The book includes concrete examples of global and local representations of GL(n), and presents their associated L-functions. In Volume 1, the theory is developed from first principles for GL(1), then carefully extended to GL(2) with complete detailed proofs of key theorems. Several proofs are presented for the first time, including Jacquet's simple and elegant proof of the tensor product theorem. In Volume 2, the higher rank situation of GL(n) is given a detailed treatment. Containing numerous exercises by Xander Faber, this book will motivate students and researchers to begin working in this fertile field of research.
Author : Anton Deitmar
Publisher : Springer Science & Business Media
Page : 255 pages
File Size : 11,95 MB
Release : 2012-08-29
Category : Mathematics
ISBN : 144714435X
Automorphic forms are an important complex analytic tool in number theory and modern arithmetic geometry. They played for example a vital role in Andrew Wiles's proof of Fermat's Last Theorem. This text provides a concise introduction to the world of automorphic forms using two approaches: the classic elementary theory and the modern point of view of adeles and representation theory. The reader will learn the important aims and results of the theory by focussing on its essential aspects and restricting it to the 'base field' of rational numbers. Students interested for example in arithmetic geometry or number theory will find that this book provides an optimal and easily accessible introduction into this topic.
Author : Toshiyuki Kobayashi
Publisher : Springer Science & Business Media
Page : 220 pages
File Size : 25,93 MB
Release : 2007-10-10
Category : Mathematics
ISBN : 0817646469
This volume uses a unified approach to representation theory and automorphic forms. It collects papers, written by leading mathematicians, that track recent progress in the expanding fields of representation theory and automorphic forms and their association with number theory and differential geometry. Topics include: Automorphic forms and distributions, modular forms, visible-actions, Dirac cohomology, holomorphic forms, harmonic analysis, self-dual representations, and Langlands Functoriality Conjecture, Both graduate students and researchers will find inspiration in this volume.
Author : Henryk Iwaniec
Publisher : American Mathematical Soc.
Page : 274 pages
File Size : 33,71 MB
Release : 1997
Category : Mathematics
ISBN : 0821807773
This volume discusses various perspectives of the theory of automorphic forms drawn from the author's notes from a Rutgers University graduate course. In addition to detailed and often nonstandard treatment of familiar theoretical topics, the author also gives special attention to such subjects as theta- functions and representatives by quadratic forms. Annotation copyrighted by Book News, Inc., Portland, OR
Author : Freydoon Shahidi
Publisher : American Mathematical Soc.
Page : 218 pages
File Size : 29,25 MB
Release : 2010
Category : Mathematics
ISBN : 0821849891
This book presents a treatment of the theory of $L$-functions developed by means of the theory of Eisenstein series and their Fourier coefficients, a theory which is usually referred to as the Langlands-Shahidi method. The information gathered from this method, when combined with the converse theorems of Cogdell and Piatetski-Shapiro, has been quite sufficient in establishing a number of new cases of Langlands functoriality conjecture; at present, some of these cases cannot be obtained by any other method. These results have led to far-reaching new estimates for Hecke eigenvalues of Maass forms, as well as definitive solutions to certain problems in analytic and algebraic number theory. This book gives a detailed treatment of important parts of this theory, including a rather complete proof of Casselman-Shalika's formula for unramified Whittaker functions as well as a general treatment of the theory of intertwining operators. It also covers in some detail the global aspects of the method as well as some of its applications to group representations and harmonic analysis. This book is addressed to graduate students and researchers who are interested in the Langlands program in automorphic forms and its connections with number theory.