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.
An Introduction to the Langlands Program
and over one million other books are available for Amazon Kindle.
Learn more
FREE Two-Day Shipping for students on millions of items. Learn more |
| ||||||||||||||||||||||||
Book Description
Special Offers and Product Promotions
- Buy $50 in qualifying physical textbooks, get $5 in Amazon MP3 Credit. Here's how (restrictions apply)
Frequently Bought Together
Editorial Reviews
Review
From the reviews: "The six chapters of this monograph give 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. First-year graduate students and researchers will benefit from this beautiful text." --Zentralblatt Math ". . . the present volume constitutes the most readable entree into the subject to date, suitable both for serious reading and for browsing, and should attract a new generation to this exciting subject. . . . Recommended." --CHOICE “I suspect this book will find its way into the hands of many graduate students. Perhaps it will also motivate a few of them to learn more, get involved, and make their own contributions.” (MAA REVIEWS)
From the Back Cover
For the past several decades the theory of automorphic forms has become a major focal point of development in number theory and algebraic geometry, with applications in many diverse areas, including combinatorics and mathematical physics. The twelve chapters of this monograph present 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. Key features of this self-contained presentation: A variety of areas in number theory from the classical zeta function up to the Langlands program are covered. The exposition is systematic, with each chapter focusing on a particular topic devoted to special cases of the program: • Basic zeta function of Riemann and its generalizations to Dirichlet and Hecke L-functions, class field theory and some topics on classical automorphic functions (E. Kowalski) • A study of the conjectures of Artin and Shimura–Taniyama–Weil (E. de Shalit) • An examination of classical modular (automorphic) L-functions as GL(2) functions, bringing into play the theory of representations (S.S. Kudla) • Selberg's theory of the trace formula, which is a way to study automorphic representations (D. Bump) • Discussion of cuspidal automorphic representations of GL(2,(A)) leads to Langlands theory for GL(n) and the importance of the Langlands dual group (J.W. Cogdell) • An introduction to the geometric Langlands program, a new and active area of research that permits using powerful methods of algebraic geometry to construct automorphic sheaves (D. Gaitsgory) Graduate students and researchers will benefit from this beautiful text.
Product Details
Would you like to update product info or give feedback on images?
|
Customer Reviews
|
There are no customer reviews yet.
|
|||
|
Video reviews
|
Inside This Book
(learn more)
First Sentence:
In this first chapter we will define and describe, in a roughly chronological order from the time of Euler to that of Hecke, some interesting classes of holomorphic functions with strange links to many aspects of number theory. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
incomplete theta series, automorphic side, continuous additive character, functorial lift, automorphic induction, irreducible admissible representation, cuspidal functions, unramified representations, admissible homomorphisms, nonarchimedean case, cuspidal representations, exceptional eigenvalues, automorphic representations, nonarchimedean local field, local functional equations, zeta integrals, cuspidal automorphic representation, semisimple conjugacy classes, global class field theory, automorphic forms, implied constant depending, archimedean theory, function field case, number field case, local class field theory Key Phrases - Capitalized Phrases (CAPs): (learn more)
New York, Academic Press, Princeton University Press, Artin L-functions, Cambridge University Press, Hecke L-functions, Dirichlet L-functions, Duke Math, Graduate Texts, Proceedings of Symposia, Algebraic Number Fields, American Mathematical Society, Johns Hopkins University Press, Semisimple Lie Groups, Annals of Mathematics Studies, Bestimmung Dirichletscher Reihen, John Wiley, Proceedings of the Durham Symposium, Springer Verlag New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Back Cover | Surprise Me!
In this first chapter we will define and describe, in a roughly chronological order from the time of Euler to that of Hecke, some interesting classes of holomorphic functions with strange links to many aspects of number theory. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
incomplete theta series, automorphic side, continuous additive character, functorial lift, automorphic induction, irreducible admissible representation, cuspidal functions, unramified representations, admissible homomorphisms, nonarchimedean case, cuspidal representations, exceptional eigenvalues, automorphic representations, nonarchimedean local field, local functional equations, zeta integrals, cuspidal automorphic representation, semisimple conjugacy classes, global class field theory, automorphic forms, implied constant depending, archimedean theory, function field case, number field case, local class field theory Key Phrases - Capitalized Phrases (CAPs): (learn more)
New York, Academic Press, Princeton University Press, Artin L-functions, Cambridge University Press, Hecke L-functions, Dirichlet L-functions, Duke Math, Graduate Texts, Proceedings of Symposia, Algebraic Number Fields, American Mathematical Society, Johns Hopkins University Press, Semisimple Lie Groups, Annals of Mathematics Studies, Bestimmung Dirichletscher Reihen, John Wiley, Proceedings of the Durham Symposium, Springer Verlag New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Back Cover | Surprise Me!
Citations (learn more)
This book cites 31
books:
See all 31 books this book cites
6
books
cite this book:
See all 6 books citing this book
- Number Theory: An approach through history from Hammurapi to Legendre by André Weil on 8 pages
- Automorphic Forms and Representations (Cambridge Studies in Advanced Mathematics) by Daniel Bump on 4 pages
- Class Field Theory (Advanced Book Classics) by Emil Artin on page 79, page 81, and page 189
- Algebraic Number Theory (Cambridge Studies in Advanced Mathematics) by A. Fröhlich on page 70, page 109, and page 192
- Algebraic Number Theory (Graduate Texts in Mathematics) by Serge Lang on page 70, page 131, and page 280
See all 31 books this book cites
- Automorphic Forms and L-Functions for the Group GL(n,R) (Cambridge Studies in Advanced Mathematics) by Dorian Goldfeld in Back Matter (1), and Back Matter (2)
- Doing Mathematics: Convention, Subject, Calculation, Analogy by Martin H. Krieger in Back Matter
- Logic, Epistemology, and the Unity of Science by Shahid Rahman on page 253
- The Honors Class: Hilbert's Problems and Their Solvers by Ben Yandell in Back Matter
- Moonshine beyond the Monster: The Bridge Connecting Algebra, Modular Forms and Physics (Cambridge Monographs on Mathematical Physics) by Terry Gannon in Back Matter
See all 6 books citing this book
Books on Related Topics
(learn more)
|
What Other Items Do Customers Buy After Viewing This Item?
Tags Customers Associate with This Product(What's this?)Click on a tag to find related items, discussions, and people.
|
Customer Discussions
|
This product's forum
Active discussions in related forums
Search Customer Discussions
|
Related forums
|
Listmania!
|
|
