Modern analysis of automorphic forms by example

著者

    • Garrett, Paul

書誌事項

Modern analysis of automorphic forms by example

Paul Garrett

（Cambridge studies in advanced mathematics, 173-174）

Cambridge University Press, 2018

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

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注記

Includes bibliographical references and index

内容説明・目次

巻冊次

v. 1 : hardback ISBN 9781107154001

内容説明

This is Volume 1 of a two-volume book that provides a self-contained introduction to the theory and application of automorphic forms, using examples to illustrate several critical analytical concepts surrounding and supporting the theory of automorphic forms. The two-volume book treats three instances, starting with some small unimodular examples, followed by adelic GL2, and finally GLn. Volume 1 features critical results, which are proven carefully and in detail, including discrete decomposition of cuspforms, meromorphic continuation of Eisenstein series, spectral decomposition of pseudo-Eisenstein series, and automorphic Plancherel theorem. Volume 2 features automorphic Green's functions, metrics and topologies on natural function spaces, unbounded operators, vector-valued integrals, vector-valued holomorphic functions, and asymptotics. With numerous proofs and extensive examples, this classroom-tested introductory text is meant for a second-year or advanced graduate course in automorphic forms, and also as a resource for researchers working in automorphic forms, analytic number theory, and related fields.

目次

  • 1. Four small examples
  • 2. The quotient Z+GL2(k)/GL2(A)
  • 3. SL3(Z), SL5(Z)
  • 4. Invariant differential operators
  • 5. Integration on quotients
  • 6. Action of G on function spaces on G
  • 7. Discrete decomposition of cuspforms
  • 8. Moderate growth functions, theory of the constant term
  • 9. Unbounded operators on Hilbert spaces
  • 10. Discrete decomposition of pseudo-cuspforms
  • 11. Meromorphic continuation of Eisenstein series
  • 12. Global automorphic Sobolev spaces, Green's functions
  • 13. Examples - topologies on natural function spaces
  • 14. Vector-valued integrals
  • 15. Differentiable vector-valued functions
  • 16. Asymptotic expansions.
巻冊次

v. 2 : hardback ISBN 9781108473842

内容説明

This is Volume 2 of a two-volume book that provides a self-contained introduction to the theory and application of automorphic forms, using examples to illustrate several critical analytical concepts surrounding and supporting the theory of automorphic forms. The two-volume book treats three instances, starting with some small unimodular examples, followed by adelic GL2, and finally GLn. Volume 2 features critical results, which are proven carefully and in detail, including automorphic Green's functions, metrics and topologies on natural function spaces, unbounded operators, vector-valued integrals, vector-valued holomorphic functions, and asymptotics. Volume 1 features discrete decomposition of cuspforms, meromorphic continuation of Eisenstein series, spectral decomposition of pseudo-Eisenstein series, and automorphic Plancherel theorem. With numerous proofs and extensive examples, this classroom-tested introductory text is meant for a second-year or advanced graduate course in automorphic forms, and also as a resource for researchers working in automorphic forms, analytic number theory, and related fields.

目次

  • 1. Unbounded operators on Hilbert spaces
  • 2. Discrete decomposition of pseudo-cuspforms
  • 3. Meromorphic continuation of Eisenstein series
  • 4. Global automorphic Sobolev spaces, Green's functions
  • 5. Examples - topologies on natural function spaces
  • 6. Vector-valued integrals
  • 7. Differentiable vector-valued functions
  • 8. Asymptotic expansions.

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