Analytic Properties of Automorphic L-Functions (eBook)

Stephen Gelbart, Freydoon Shahidi (Autoren)

J. Coates, S. Helgason (Herausgeber)

eBook Download: PDF

2014 | 1. Auflage
142 Seiten
Elsevier Science (Verlag)
978-1-4832-6103-4 (ISBN)

Infos

Analytic Properties of Automorphic L-Functions is a three-chapter text that covers considerable research works on the automorphic L-functions attached by Langlands to reductive algebraic groups. Chapter I focuses on the analysis of Jacquet-Langlands methods and the Einstein series and Langlands' so-called 'Euler products. This chapter explains how local and global zeta-integrals are used to prove the analytic continuation and functional equations of the automorphic L-functions attached to GL(2). Chapter II deals with the developments and refinements of the zeta-inetgrals for GL(n). Chapter III describes the results for the L-functions L (s, ?, r), which are considered in the constant terms of Einstein series for some quasisplit reductive group. This book will be of value to undergraduate and graduate mathematics students.

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Analytic Properties of Automorphic L-Functions is a three-chapter text that covers considerable research works on the automorphic L-functions attached by Langlands to reductive algebraic groups. Chapter I focuses on the analysis of Jacquet-Langlands methods and the Einstein series and Langlands' so-called "e;Euler products. This chapter explains how local and global zeta-integrals are used to prove the analytic continuation and functional equations of the automorphic L-functions attached to GL(2). Chapter II deals with the developments and refinements of the zeta-inetgrals for GL(n). Chapter III describes the results for the L-functions L (s, ?, r), which are considered in the constant terms of Einstein series for some quasisplit reductive group. This book will be of value to undergraduate and graduate mathematics students.

Inhalt

Front Cover 1
Analytic Properties of Automorphic L-Functions 
4 
Copyright Page 5
Table of Contents 6
Acknowledgements 8
INTRODUCTION 10
CHAPTER I. FIRST STEPS (1965-1970) 14
§1. AN ANALYSIS OF THE METHOD OF JACQUET-LANGLANDS 14
§2. EISENSTEIN SERIES L· LANGLANDS' "EULER PRODUCTS" 30
CHAPTER II. DEVELOPMENTS AND REFINEMENTS (1970-1982) 50
§1. ZETA-INTEGRALS FOR GL(n) AND BEYOND 50
§2. EISENSTEIN SERIES AND GENERIC REPRESENTATIONS 84
CHAPTER III. RECENT DEVELOPMENTS (1982- ) 96
§1. EXPLICIT CONSTRUCTION OF ZETA-FUNCTIONS Á LA PIATETSKI-SHAPIRO 96
§2. LANGLANDS' THEORY COMPLETED 111
REFERENCES 128
INDEX 138
Perspectives in Mathematics 142

Produkt-Details

• Erscheint lt. Verlag: 14.7.2014
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Technik
• ISBN-10: 1-4832-6103-4 / 1483261034
• ISBN-13: 978-1-4832-6103-4 / 9781483261034