Meromorphic Continuation and Functional Equations of Cuspidal Eisenstein Series for Maximal Cuspidal Subgroups.

Intro -- TABLE OF CONTENTS -- INTRODUCTION -- CHAPTER 1 THE DEFINITION AND BASIC PROPERTIES OF THE EISENSTEIN SERIES -- 1.1. Introduction -- 1.2. Prerequisites for the Eisenstein Series -- 1.3. The Eisenstein Series -- 1.4. Selberg's Eigenfunction Principle -- CHAPTER 2 THE COMPACT OPERATORS -- 2.1. Introduction -- 2.2. Construction of Kernel -- 2.3. Convolutions on L[sup(2)](Γ \ G) -- 2.4. Definition of Compact Operators -- CHAPTER 3 FREDHOLM EQUATIONS -- 3.1. Introduction -- 3.2. The Constant Terms of Eisenstein Series -- 3.3. Convolution with Functions Depending on a Complex Parameter -- 3.4. Projection of the Constant Terms of Eisenstein Series -- 3.5. Truncation of the Eisenstein Series -- 3.6. Holomorphicity of Fredholm Solutions -- CHAPTER 4 ANALYTIC CONTINUATION -- 4.1. Introduction -- 4.2. A System of Linear Equations in φ(J | Λ) -- 4.3. Uniqueness of Solution -- 4.4. Meromorphicity of φ(J | Λ) and the Eisenstein Series -- CHAPTER 5 FUNCTIONAL EQUATIONS -- 5.1. Introduction -- 5.2. Functional Equations -- CHAPTER 6 THE GENERAL CASE OF SEVERAL CUSPS -- 6.1. Introduction -- 6.2. The Definition and Basic Properties of the Eisenstein Series -- 6.3. The Compact Operators -- 6.4. Fredholm Equations -- 6.5. Analytic Continuation -- 6.6. Functional Equations -- REFERENCES.

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