Overview

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. Covered are a variety of areas in number theory from the classical zeta function up to the Langlands program. The exposition is sytematic, with each chapter focusing on a particular topic devoted to special cases of the program, and accessible to graduate students and researchers in the field.

Full Product Details

Author:   Joseph Bernstein ,  S.S. Kudla ,  Stephen Gelbart ,  E. Kowalski
Publisher:   Birkhauser Boston Inc
Imprint:   Birkhauser Boston Inc
Edition:   2004 ed.
Dimensions:   Width: 15.50cm , Height: 1.50cm , Length: 23.50cm
Weight:   0.910kg
ISBN:  

9780817632113

ISBN 10:   0817632115
Pages:   281
Publication Date:   20 May 2003
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

Preface * E. Kowalski - Elementary Theory of L-Functions I * E. Kowalski - Elementary Theory of L-Functions II * E. Kowalski - Classical Automorphic Forms * E. DeShalit - Artin L-Functions * E. DeShalit - L-Functions of Elliptic Curves and Modular Forms * S. Kudla - Tate's Thesis * S. Kudla - From Modular Forms to Automorphic Representations * D. Bump - Spectral Theory and the Trace Formula * J. Cogdell - Analytic Theory of L-Functions for GLn * J. Cogdell - Langlands Conjectures for GLn * J. Cogdell - Dual Groups and Langlands Functoriality * D. Gaitsgory - Informal Introduction to Geometric Langlands

Reviews

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 reviews: <p> 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. <p>--Zentralblatt Math <p>. . . 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. <p>--CHOICE <p>a oeI 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.a (MAA REVIEWS)

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