An Introduction to the Langlands Program (eBook, PDF)

Redaktion: Bernstein, Joseph; Gelbart, Stephen

• Format: PDF

Produktbeschreibung

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 beautifultext.

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Produktdetails

• Verlag: Birkhäuser Boston
• Seitenzahl: 281
• Erscheinungstermin: 11. Dezember 2013
• Englisch
• ISBN-13: 9780817682262
• Artikelnr.: 44198414

Autorenporträt

Contributions by S.S. Kudla, E. Kowalski, E. de Shalit, D. Gaitsgory, J.W. Cogdell und D. Bump

Inhaltsangabe

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.

Rezensionen

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)