An Introduction to Automorphic Representations With a view toward trace formulae /
The goal of this textbook is to introduce and study automorphic representations, objects at the very core of the Langlands Program. It is designed for use as a primary text for either a semester or a year-long course, for the independent study of advanced topics, or as a reference for researchers. T...
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| Main Authors: | , |
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| 格式: | 電子 電子書 |
| 語言: | 英语 |
| 出版: |
Cham :
Springer International Publishing : Imprint: Springer,
2024.
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| 版: | 1st ed. 2024. |
| 叢編: | Graduate Texts in Mathematics,
300 |
| 主題: | |
| 在線閱讀: | https://doi.org/10.1007/978-3-031-41153-3 |
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書本目錄:
- 1. Affine Algebraic Groups
- 2. Adeles
- 3. Discrete Automorphic Representations
- 4. Archimedean Representation Theory
- 5. Representations of Totally Disconnected Groups
- 6. Automorphic Forms
- 7. Unramified Representations
- 8. Nonarchimedean Representation Theory
- 9. The Cuspidal Spectrum
- 10. Einsenstein Series
- 11. Rankin-Selberg L-functions
- 12. Langlands Functoriality
- 13. Known Cases of Global Langlands Functoriality
- 14. Distinction and Period Integrals
- 15. The Cohomology of Locally Symmetric Spaces
- 16. Spectral Sides of the Trace Formulae
- 17. Orbital Integrals
- 18. Simple Trace Formulae
- 19. Applications of Trace Formulae
- A. Groups attached to involutions of algebras
- B. The Iwasawa Decomposition
- C. Poisson Summation
- D. Alternate conventions related to adelic quotients
- Hints to selected exercises
- References
- Index.