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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

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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