Contents
Chapter 1. Introduction 1
Chapter 2. Degree 16 Standard L-function of GSp{2) x GSp{2) 17
1. Preliminaries 17
2. Global Integral of Rankin-Selberg Type 20
3. Unramified Local Zeta Integrals 27
4. Local Langlands Factor of Degree 16 for GSp{2) x GSp{2) 37
5. The Fundamental Identity 68
Chapter 3. Poles of Eisenstein Series of Sp(n) 71
1. The Pf-constant Term of Eisenstein Series 71
2. Local Analyses of Intertwining Operators 76
3. Poles of Eisenstein Series: n 3 94
4. Poles of Eisenstein Series 108
5. Proof of Two Lemmas 112
Chapter 4. Residue Representations of Eisenstein Series 121
1. Eisenstein Series of Sp(4) 121
2. Intertwining Operators and Quasi-invariant Distributions 123
3. Residues of Eisenstein Series E^(g,s; fs) 143
4. Analytic Properties of the Global Integral 149
Chapter 5. Local Theory of Rankin-Selberg Convolution 153
1. Some Estimates 153
2. Nonvanishing of Local Zeta Integrals 162
3. Absolutely Convergence of Local Zeta Integrals 171
4. Meromorphic Continuation of Local Zeta Integrals 178
Bibliography 187
Index 194
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