Automorphic representations and L-functions for the general linear group

著者

書誌事項

Automorphic representations and L-functions for the general linear group

Dorian Goldfeld, Joseph Hundley ; with exercises by Xander Faber

（Cambridge studies in advanced mathematics, 129-130）

Cambridge University Press, 2011

  • v. 1 : hardback
  • v. 2 : hardback

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注記

Each vol. includes bibliographical references and indexes

内容説明・目次

巻冊次

v. 1 : hardback ISBN 9780521474238

内容説明

This graduate-level textbook provides an elementary exposition of the theory of automorphic representations and L-functions for the general linear group in an adelic setting. Definitions are kept to a minimum and repeated when reintroduced so that the book is accessible from any entry point, and with no prior knowledge of representation theory. The book includes concrete examples of global and local representations of GL(n), and presents their associated L-functions. In Volume 1, the theory is developed from first principles for GL(1), then carefully extended to GL(2) with complete detailed proofs of key theorems. Several proofs are presented for the first time, including Jacquet's simple and elegant proof of the tensor product theorem. In Volume 2, the higher rank situation of GL(n) is given a detailed treatment. Containing numerous exercises by Xander Faber, this book will motivate students and researchers to begin working in this fertile field of research.

目次

  • Preface
  • 1. Adeles over Q
  • 2. Automorphic representations and L-functions for GL(1,AQ)
  • 3. The classical theory of automorphic forms for GL(2)
  • 4. Automorphic forms for GL(2,AQ)
  • 5. Automorphic representations for GL(2,AQ)
  • 6. Theory of admissible representations of GL(2,Qp)
  • 7. Theory of admissible (g,K ) modules for GL(2,R)
  • 8. The contragredient representation for GL(2)
  • 9. Unitary representations of GL(2)
  • 10. Tensor products of local representations
  • 11. The Godement-Jacquet L-function for GL(2,AQ)
  • Solutions to selected exercises
  • References
  • Symbols index
  • Index.
巻冊次

v. 2 : hardback ISBN 9781107007994

内容説明

This graduate-level textbook provides an elementary exposition of the theory of automorphic representations and L-functions for the general linear group in an adelic setting. Definitions are kept to a minimum and repeated when reintroduced so that the book is accessible from any entry point, and with no prior knowledge of representation theory. The book includes concrete examples of global and local representations of GL(n), and presents their associated L-functions. In Volume 1, the theory is developed from first principles for GL(1), then carefully extended to GL(2) with complete detailed proofs of key theorems. Several proofs are presented for the first time, including Jacquet's simple and elegant proof of the tensor product theorem. In Volume 2, the higher rank situation of GL(n) is given a detailed treatment. Containing numerous exercises by Xander Faber, this book will motivate students and researchers to begin working in this fertile field of research.

目次

  • Preface
  • 1. The classical theory of automorphic forms for GL(n,R)
  • 2. Automorphic forms and representations for GL(n,AQ)
  • 3. Theory of local representations for GL(n)
  • 4. The Godement-Jacquet L-function for GL(n,AQ)
  • Solutions to selected exercises
  • References
  • Symbols index
  • Index.

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