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Poles and residues of Eisenstein series for symplectic and unitary groups
About this Title
Paul Feit
Publication: Memoirs of the American Mathematical Society
Publication Year:
1986; Volume 61, Number 346
ISBNs: 978-0-8218-2347-7 (print); 978-1-4704-0762-9 (online)
DOI: https://doi.org/10.1090/memo/0346
MathSciNet review: 840834
MSC: Primary 11F55; Secondary 11F30
Table of Contents
Chapters
- Introduction
- 0. Notation
- 1. Definition of the Eisenstein series
- Part I. Formal Dirichlet series
- 2. Preliminaries on semi-simple algebras
- 3. Local unitary groups
- 4. A theorem on Dirichlet series
- 5. Representations of one form by another
- 6. Explicit computations: SP and SU cases
- 7. A special argument for $\alpha _1$
- Part II. The finiteness problem
- 8. Notation
- 9. Finiteness theorems
- 10. The Fourier coefficients
- 11. The $\Gamma$-factor calculation
- 12. Three remarks
- 13. The proof of Theorem 9.1
- Part III. Analyticity
- 14. Positive Fourier expansions
- Part IV. Algebraic properties
- 15. A rationality criterion
- 16. The transfer map
- 17. Stong approximation
- 18. Proofs of Theorems 15.1 and 15.2