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Author : H. Jacquet
Publisher : Springer
Page : 156 pages
File Size : 55,7 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540376125
Author : D. Bump
Publisher : Springer
Page : 196 pages
File Size : 52,9 Mb
Release : 2006-12-08
Category : Mathematics
ISBN : 9783540390558
Author : H. Jacquet,R. P. Langlands
Publisher : Lecture Notes in Mathematics
Page : 1102 pages
File Size : 53,8 Mb
Release : 1970
Category : Mathematics
ISBN : CORNELL:31924001511579
Author : H. Jacquet,R. P. Langlands
Publisher : Unknown
Page : 564 pages
File Size : 49,6 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662204010
Author : Dorian Goldfeld
Publisher : Cambridge University Press
Page : 65 pages
File Size : 40,6 Mb
Release : 2006-08-03
Category : Mathematics
ISBN : 9781139456203
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 : H. Jacquet
Publisher : Unknown
Page : 164 pages
File Size : 52,7 Mb
Release : 2014-09-01
Category : Electronic
ISBN : 3662205874
Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 40,6 Mb
Release : 1972
Category : Electronic
ISBN : OCLC:636736629
Author : Hervé Jacquet
Publisher : Unknown
Page : 548 pages
File Size : 48,9 Mb
Release : 1970
Category : Automorphic forms
ISBN : OCLC:1088751683
Author : Armand Borel,W. Casselman,American Mathematical Society
Publisher : American Mathematical Soc.
Page : 394 pages
File Size : 48,6 Mb
Release : 1979-06-30
Category : Mathematics
ISBN : 9780821814376
Part 2 contains sections on Automorphic representations and $L$-functions, Arithmetical algebraic geometry and $L$-functions
Author : Stephen S. Gelbart
Publisher : Princeton University Press
Page : 227 pages
File Size : 41,9 Mb
Release : 2016-03-02
Category : Mathematics
ISBN : 9781400881611
This volume investigates the interplay between the classical theory of automorphic forms and the modern theory of representations of adele groups. Interpreting important recent contributions of Jacquet and Langlands, the author presents new and previously inaccessible results, and systematically develops explicit consequences and connections with the classical theory. The underlying theme is the decomposition of the regular representation of the adele group of GL(2). A detailed proof of the celebrated trace formula of Selberg is included, with a discussion of the possible range of applicability of this formula. Throughout the work the author emphasizes new examples and problems that remain open within the general theory. TABLE OF CONTENTS: 1. The Classical Theory 2. Automorphic Forms and the Decomposition of L2(PSL(2,R) 3. Automorphic Forms as Functions on the Adele Group of GL(2) 4. The Representations of GL(2) over Local and Global Fields 5. Cusp Forms and Representations of the Adele Group of GL(2) 6. Hecke Theory for GL(2) 7. The Construction of a Special Class of Automorphic Forms 8. Eisenstein Series and the Continuous Spectrum 9. The Trace Formula for GL(2) 10. Automorphic Forms on a Quaternion Algebr?
Author : Anton Deitmar
Publisher : Springer Science & Business Media
Page : 255 pages
File Size : 46,8 Mb
Release : 2012-08-29
Category : Mathematics
ISBN : 9781447144359
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 : Werner Müller,Sug Woo Shin,Nicolas Templier
Publisher : Springer
Page : 578 pages
File Size : 45,7 Mb
Release : 2016-09-20
Category : Mathematics
ISBN : 9783319414249
Featuring the work of twenty-three internationally-recognized experts, this volume explores the trace formula, spectra of locally symmetric spaces, p-adic families, and other recent techniques from harmonic analysis and representation theory. Each peer-reviewed submission in this volume, based on the Simons Foundation symposium on families of automorphic forms and the trace formula held in Puerto Rico in January-February 2014, is the product of intensive research collaboration by the participants over the course of the seven-day workshop. The goal of each session in the symposium was to bring together researchers with diverse specialties in order to identify key difficulties as well as fruitful approaches being explored in the field. The respective themes were counting cohomological forms, p-adic trace formulas, Hecke fields, slopes of modular forms, and orbital integrals.
Author : Stephen S. Gelbart
Publisher : Princeton University Press
Page : 284 pages
File Size : 53,9 Mb
Release : 1975-03-21
Category : Mathematics
ISBN : 0691081565
This volume investigates the interplay between the classical theory of automorphic forms and the modern theory of representations of adele groups. Interpreting important recent contributions of Jacquet and Langlands, the author presents new and previously inaccessible results, and systematically develops explicit consequences and connections with the classical theory. The underlying theme is the decomposition of the regular representation of the adele group of GL(2). A detailed proof of the celebrated trace formula of Selberg is included, with a discussion of the possible range of applicability of this formula. Throughout the work the author emphasizes new examples and problems that remain open within the general theory. TABLE OF CONTENTS: 1. The Classical Theory 2. Automorphic Forms and the Decomposition of L2(PSL(2,R) 3. Automorphic Forms as Functions on the Adele Group of GL(2) 4. The Representations of GL(2) over Local and Global Fields 5. Cusp Forms and Representations of the Adele Group of GL(2) 6. Hecke Theory for GL(2) 7. The Construction of a Special Class of Automorphic Forms 8. Eisenstein Series and the Continuous Spectrum 9. The Trace Formula for GL(2) 10. Automorphic Forms on a Quaternion Algebr?
Author : Gaëtan Chenevier,Jean Lannes
Publisher : Springer
Page : 417 pages
File Size : 52,8 Mb
Release : 2019-02-28
Category : Mathematics
ISBN : 9783319958910
This book includes a self-contained approach of the general theory of quadratic forms and integral Euclidean lattices, as well as a presentation of the theory of automorphic forms and Langlands' conjectures, ranging from the first definitions to the recent and deep classification results due to James Arthur. Its connecting thread is a question about lattices of rank 24: the problem of p-neighborhoods between Niemeier lattices. This question, whose expression is quite elementary, is in fact very natural from the automorphic point of view, and turns out to be surprisingly intriguing. We explain how the new advances in the Langlands program mentioned above pave the way for a solution. This study proves to be very rich, leading us to classical themes such as theta series, Siegel modular forms, the triality principle, L-functions and congruences between Galois representations. This monograph is intended for any mathematician with an interest in Euclidean lattices, automorphic forms or number theory. A large part of it is meant to be accessible to non-specialists.
Author : Joseph Bernstein,Stephen Gelbart
Publisher : Springer Science & Business Media
Page : 283 pages
File Size : 49,7 Mb
Release : 2013-12-11
Category : Mathematics
ISBN : 9780817682262
This book presents a broad, user-friendly introduction to the Langlands program, that is, the theory of automorphic forms and its connection with the theory of L-functions and other fields of mathematics. Each of the twelve chapters focuses on a particular topic devoted to special cases of the program. The book is suitable for graduate students and researchers.
